user10718: Isn't it possible that whatever they have realised is just a psychological effect? Doing continuously hard practices leads to affect their mind and they tend to believe that, yes, this is the truth. They started lying to themselves that they know the truth?
I truly respect their teachings which shows us the path to live a good life. I am just talking about the real truth (if there is any).
With love.

user8157: The truth of the Buddha is the method to end suffering. When a person tests the method & it works, they know the truth of the method, similar to when medicine is effective in curing in a sickness. 
In Buddhism, there is no truth apart from personal verification, as taught: 

"Knowing thus and seeing thus, would you say, 'The Teacher is our respected mentor. We speak thus out of respect for the Teacher'?"
"No, lord."
"Knowing thus and seeing thus, would you say, 'The Contemplative says this. We speak thus in line with the Contemplative's words'?"
"No, lord."
"Knowing thus and seeing thus, would you dedicate yourselves to another teacher?"
"No, lord."
"Knowing thus and seeing thus, would you return to the observances,
  grand ceremonies, & auspicious rites of common contemplatives &
  brahmans as having any essence?"
"No, lord."
"Is it the case that you speak simply in line with what you have known, seen, & understood for yourselves?"
"Yes, lord."
"Good, monks. You have been guided by me in this Dhamma which is to be seen here & now, timeless, inviting verification, pertinent, to be
  realized by the observant for themselves. For it has been said, 'This
  Dhamma is to be seen here & now, timeless, inviting verification,
  pertinent, to be by the observant for themselves,' and it was in
  reference to this that it was said.
Mahatanhasankhaya Sutta


user295: Wisdom and the faith inspired by it is 3 folds:

what is learned
what is logically deduced 
what is experienced

Until you have experienced you will not know for sure. The real truth is revealed to you through your Vipassana meditation.
Brahmajala Sutta discusses instances where false ideas arose through misinterpreting experiences, some being meditative.
Generally people who have realised the truth do not brag about it so you will never know. If they grab about it then it is most likely they have not. Also discussing about another's attainment does not help oneself hence best left aside. Also even if you are still not realised the truth, saying does not serve any practical purpose, and if the situation changes your response will have to change indirectly giving away you have at the time achieved something. 

user7309: As to your title question, MN27 - http://www.accesstoinsight.org/tipitaka/mn/mn.027.than.html gives an account how every achievement before Nibbana, is no thing more than a clue as to the accuracy of the Buddha's insight. Prior to the attainment of arahantship, 'Truth' is not to be realised. 
Practicing the same thing over and over again does make the mind 'run in that context' even outside of intentionally concentrating on that subject - I used to dream about weiqi when I used to play 4 hours a day.. In this respect, some aspect of Buddhist literature may be interpreted as only psychological (monks meditating and reaching the Tusita heaven etc.. Though these states are only ever acknowledged as psychological within Buddhism). 
The difficulty with your point is that, if you skip annihalationism (nihilism), and embrace mundane 'right view', or:

"And what is the right view with effluents, siding with merit,
  resulting in acquisitions? 'There is what is given, what is offered,
  what is sacrificed. There are fruits & results of good & bad actions.
  There is this world & the next world. There is mother & father. There
  are spontaneously reborn beings; there are contemplatives & brahmans
  who, faring rightly & practicing rightly, proclaim this world & the
  next after having directly known & realized it for themselves.' This
  is the right view with effluents, siding with merit, resulting in
  acquisitions." -  MN117

'truth' becomes evident. And if there are 'good and bad actions', there is a path  that can skip the bad and keep to the good ones (assuming beings capable of discerning between the two). Would it then be reasonable to define 'Truth', having established 'truth', and a Path towards it? 
From my reading of the Suttas, the Buddha did not pursue the concept of Truth. For one, in the Potthapada Sutta, the Buddha talks about 'exclusively happy states', which is how an Absolute state of Happiness (a Christian heaven?) would have to manifest (http://www.accesstoinsight.org/tipitaka/dn/dn.09.0.than.html):

"There are some brahmans & contemplatives with a doctrine & view like
  this: 'After death, the self is exclusively happy and free from
  disease.' I approached them and asked them, 'Is it true that you have
  a doctrine & view like this: "After death, the self is exclusively
  happy and free from disease"?' When asked this, they replied, 'Yes.'
  So I asked them, 'But do you dwell having known or seen an exclusively
  happy world?' When asked this, they said, 'No.' So I asked them, 'But
  have you ever been aware of a self exclusively happy for a day or a
  night, or for half a day or half a night?' When asked this, they said,
  'No.' So I asked them, 'But do you know that "This is the path, this
  is the practice for the realization of an exclusively happy world"?'
  When asked this, they said, 'No.' So I asked them, 'But have you heard
  the voices of devas reborn in an exclusively happy world, saying,
  "Practice well, my dears. Practice straightforwardly, my dears, for
  the realization of an exclusively happy world, because it was through
  such a practice that we ourselves have been reborn in an exclusively
  happy world"?' When asked this, they said, 'No.'
"So what do you think, Potthapada — when this is the case, don't the
  words of those brahmans & contemplatives turn out to be unconvincing?"
"Yes, lord. When this is the case, the words of those brahmans &
  contemplatives turn out to be unconvincing."
"Potthapada, it's as if a man were to say, 'I'm in love with the most
  beautiful woman in this country,' and other people were to say to him,
  'Well, my good man, this most beautiful woman in this country with
  whom you are in love: do you know if she's of the warrior caste, the
  priestly caste, the merchant caste, or the laborer caste?' and, when
  asked this, he would say, 'No.' Then they would say to him, 'Well
  then, do you know her name or clan name? Whether she's tall, short, or
  of medium height? Whether she's dark, fair, or ruddy-skinned? Do you
  know what village or town or city she's from?' When asked this, he
  would say, 'No.' Then they would say to him, 'So you've never known or
  seen the woman you're in love with?' When asked this, he would say,
  'Yes.'
"So what do you think, Potthapada — when this is the case, don't the
  words of that man turn out to be unconvincing?"
"Yes, lord..."
"In the same way, there are some brahmans & contemplatives with a
  doctrine & view like this: 'After death, the self is exclusively happy
  and free from disease.'... Don't the words of those brahmans &
  contemplatives turn out to be unconvincing?"
"Yes, lord..."
"Potthapada, it's as if a man at a crossroads were to build a
  staircase for ascending to a palace, and other people were to say to
  him, 'Well, my good man, this palace for which you are building a
  staircase: do you know whether it's east, west, north, or south of
  here? Whether it's high, low, or in between?' and, when asked this, he
  would say, 'No.' Then they would say to him, 'So you don't know or see
  the palace for which you are building a staircase?' When asked this,
  he would say, 'Yes.'
"So what do you think, Potthapada — when this is the case, don't the
  words of that man turn out to be unconvincing?"
"Yes, lord..."
"In the same way, there are some brahmans & contemplatives with a
  doctrine & view like this: 'After death, the self is exclusively happy
  and free from disease.'... Don't the words of those brahmans &
  contemplatives turn out to be unconvincing?"
"Yes, lord. When this is the case, the words of those brahmans &
  contemplatives turn out to be unconvincing."

, whilst Absolutes are not Absolutely denied by the Buddha, given the empirical evidence of impermanence (and the non-self that follows), the only place where such Absolutes could be found is beyond empirical evidence - beyond experience (or Metaphysics, 'after Physics' - as Aristotle stated, with regards to the investigation of 'things' beyond evidence). As such, this Essentialist Truth - whether theistic or nihilistic - is only ever an inferred Truth - never a directly perceived Truth.. Plato's Parmeneides says as much!

".......... Then the one does not exist in such way as to be one; for if it were
  and partook of being, it would already be; but if the argument is to
  be trusted, the one neither is nor is one? 
True.  But that which is not admits of no attribute or relation?  Of
  course not. Then there is no name, nor expression, nor perception,
  nor opinion, nor knowledge of it? 
Clearly not.  Then it is neither named, nor expressed, nor opined, nor
  known, nor does anything that is perceive it. 
So we must infer.  But can all this be true about the one?  I think
  not. 
Suppose, now, that we return once more to the original hypothesis....."

(Plato gets to the same understanding that Truth must be placed beyond all perception, if it Is. But he chooses to stick with the inferred argument, rather than follow perception)
The Buddha's insight however, is to be fulfilled at its end, with perception alone, as demanded by the Kalama Sutta (http://www.accesstoinsight.org/tipitaka/an/an03/an03.065.than.html):

"Of course you are uncertain, Kalamas. Of course you are in doubt.
  When there are reasons for doubt, uncertainty is born. So in this
  case, Kalamas, don't go by reports, by legends, by traditions, by
  scripture, by logical conjecture, by inference, by analogies, by
  agreement through pondering views, by probability, or by the thought,
  'This contemplative is our teacher.' When you know for yourselves
  that, 'These qualities are unskillful; these qualities are
  blameworthy; these qualities are criticized by the wise; these
  qualities, when adopted & carried out, lead to harm & to suffering' —
  then you should abandon them."

and as fulfilled by all that become Arahats, as did Sariputta, helpfully described by the Buddha in the Anupada Sutta (http://www.accesstoinsight.org/tipitaka/mn/mn.111.than.html).
In his first sermon (http://www.accesstoinsight.org/tipitaka/sn/sn56/sn56.011.than.html) the Buddha stated the Four Noble Truths (http://www.accesstoinsight.org/ptf/dhamma/sacca/). These Truths are no thing more than declarative statements as to how the world is perceived to be. In a world that has Absolute constructs, the 'Truth' that 'all conditioned experience is suffering', is simply false. But no such world is either perceived to manifests empirically, or can be created within though without creating contradictions (for this read Nagarjuna's 'Fundamental Wisdom of the Middle Way').
The Buddha does link stress/suffering to impermanence and non-self within the Truths, and at this juncture you can definitely argue that psychology will play a part, as stress and suffering are psychological experiences, but you would have to find a mind that prefers constant change (and this includes death and rebirth) to certainty to argue that the Truths fail within the empirical world. 

10718: <p>Isn't it possible that whatever they have realised is just a psychological effect? Doing continuously hard practices leads to affect their mind and they tend to believe that, yes, this is the truth. They started lying to themselves that they know the truth?
<strong>I truly respect their teachings which shows us the path to live a good life. I am just talking about the real truth (if there is any).</strong></p>

<p>With love.</p>
 8157: <p>The truth of the Buddha is the method to end suffering. When a person tests the method &amp; it works, they know the truth of the method, similar to when medicine is effective in curing in a sickness. </p>

<p>In Buddhism, there is no truth apart from personal verification, as taught: </p>

<blockquote>
  <p><em>"Knowing thus and seeing thus, would you say, 'The Teacher is our respected mentor. We speak thus out of respect for the Teacher'?"</em></p>
  
  <p><em>"No, lord."</em></p>
  
  <p><em>"Knowing thus and seeing thus, would you say, 'The Contemplative says this. We speak thus in line with the Contemplative's words'?"</em></p>
  
  <p><em>"No, lord."</em></p>
  
  <p><em>"Knowing thus and seeing thus, would you dedicate yourselves to another teacher?"</em></p>
  
  <p><em>"No, lord."</em></p>
  
  <p>"Knowing thus and seeing thus, would you return to the observances,
  grand ceremonies, &amp; auspicious rites of common contemplatives &amp;
  brahmans as having any essence?"</p>
  
  <p><em>"No, lord."</em></p>
  
  <p><em>"Is it the case that you speak simply in line with what you have known, seen, &amp; understood for yourselves?"</em></p>
  
  <p><em>"Yes, lord."</em></p>
  
  <p><em>"Good, monks. You have been guided by me in this Dhamma which is to be seen here &amp; now, timeless, inviting verification, pertinent, to be
  realized by the observant for themselves. For it has been said, 'This
  Dhamma is to be seen here &amp; now, timeless, inviting verification,
  pertinent, to be by the observant for themselves,' and it was in
  reference to this that it was said.</em></p>
  
  <p><a href="http://www.accesstoinsight.org/tipitaka/mn/mn.038.than.html" rel="nofollow noreferrer"><em>Mahatanhasankhaya Sutta</em></a></p>
</blockquote>
 295: <p>Wisdom and the faith inspired by it is 3 folds:</p>

<ol>
<li>what is learned</li>
<li>what is logically deduced </li>
<li>what is experienced</li>
</ol>

<p>Until you have experienced you will not know for sure. The real truth is revealed to you through your Vipassana meditation.</p>

<p><a href="https://en.wikipedia.org/wiki/Brahmajala_Sutta_(Theravada)" rel="nofollow noreferrer">Brahmajala Sutta</a> discusses instances where false ideas arose through misinterpreting experiences, some being meditative.</p>

<p>Generally people who have realised the truth do not brag about it so you will never know. If they grab about it then it is most likely they have not. Also discussing about another's attainment does not help oneself hence best left aside. Also even if you are still not realised the truth, saying does not serve any practical purpose, and if the situation changes your response will have to change indirectly giving away you have at the time achieved something. </p>
 7309: <p>As to your title question, MN27 - <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.027.than.html" rel="nofollow noreferrer">http://www.accesstoinsight.org/tipitaka/mn/mn.027.than.html</a> gives an account how every achievement before Nibbana, is no thing more than a clue as to the accuracy of the Buddha's insight. Prior to the attainment of arahantship, 'Truth' is not to be realised. </p>

<p>Practicing the same thing over and over again does make the mind 'run in that context' even outside of intentionally concentrating on that subject - I used to dream about weiqi when I used to play 4 hours a day.. In this respect, some aspect of Buddhist literature may be interpreted as only psychological (monks meditating and reaching the Tusita heaven etc.. Though these states are only ever acknowledged as psychological within Buddhism). </p>

<p>The difficulty with your point is that, if you skip annihalationism (nihilism), and embrace mundane 'right view', or:</p>

<blockquote>
  <p>"And what is the right view with effluents, siding with merit,
  resulting in acquisitions? 'There is what is given, what is offered,
  what is sacrificed. There are fruits &amp; results of good &amp; bad actions.
  There is this world &amp; the next world. There is mother &amp; father. There
  are spontaneously reborn beings; there are contemplatives &amp; brahmans
  who, faring rightly &amp; practicing rightly, proclaim this world &amp; the
  next after having directly known &amp; realized it for themselves.' This
  is the right view with effluents, siding with merit, resulting in
  acquisitions." -  MN117</p>
</blockquote>

<p>'truth' becomes evident. And if there are 'good and bad actions', there is a path  that can skip the bad and keep to the good ones (assuming beings capable of discerning between the two). Would it then be reasonable to define 'Truth', having established 'truth', and a Path towards it? </p>

<p>From my reading of the Suttas, the Buddha did not pursue the concept of Truth. For one, in the Potthapada Sutta, the Buddha talks about 'exclusively happy states', which is how an Absolute state of Happiness (a Christian heaven?) would have to manifest (<a href="http://www.accesstoinsight.org/tipitaka/dn/dn.09.0.than.html" rel="nofollow noreferrer">http://www.accesstoinsight.org/tipitaka/dn/dn.09.0.than.html</a>):</p>

<blockquote>
  <p>"There are some brahmans &amp; contemplatives with a doctrine &amp; view like
  this: 'After death, the self is exclusively happy and free from
  disease.' I approached them and asked them, 'Is it true that you have
  a doctrine &amp; view like this: "After death, the self is exclusively
  happy and free from disease"?' When asked this, they replied, 'Yes.'
  So I asked them, 'But do you dwell having known or seen an exclusively
  happy world?' When asked this, they said, 'No.' So I asked them, 'But
  have you ever been aware of a self exclusively happy for a day or a
  night, or for half a day or half a night?' When asked this, they said,
  'No.' So I asked them, 'But do you know that "This is the path, this
  is the practice for the realization of an exclusively happy world"?'
  When asked this, they said, 'No.' So I asked them, 'But have you heard
  the voices of devas reborn in an exclusively happy world, saying,
  "Practice well, my dears. Practice straightforwardly, my dears, for
  the realization of an exclusively happy world, because it was through
  such a practice that we ourselves have been reborn in an exclusively
  happy world"?' When asked this, they said, 'No.'</p>
  
  <p>"So what do you think, Potthapada — when this is the case, don't the
  words of those brahmans &amp; contemplatives turn out to be unconvincing?"</p>
  
  <p>"Yes, lord. When this is the case, the words of those brahmans &amp;
  contemplatives turn out to be unconvincing."</p>
  
  <p>"Potthapada, it's as if a man were to say, 'I'm in love with the most
  beautiful woman in this country,' and other people were to say to him,
  'Well, my good man, this most beautiful woman in this country with
  whom you are in love: do you know if she's of the warrior caste, the
  priestly caste, the merchant caste, or the laborer caste?' and, when
  asked this, he would say, 'No.' Then they would say to him, 'Well
  then, do you know her name or clan name? Whether she's tall, short, or
  of medium height? Whether she's dark, fair, or ruddy-skinned? Do you
  know what village or town or city she's from?' When asked this, he
  would say, 'No.' Then they would say to him, 'So you've never known or
  seen the woman you're in love with?' When asked this, he would say,
  'Yes.'</p>
  
  <p>"So what do you think, Potthapada — when this is the case, don't the
  words of that man turn out to be unconvincing?"</p>
  
  <p>"Yes, lord..."</p>
  
  <p>"In the same way, there are some brahmans &amp; contemplatives with a
  doctrine &amp; view like this: 'After death, the self is exclusively happy
  and free from disease.'... Don't the words of those brahmans &amp;
  contemplatives turn out to be unconvincing?"</p>
  
  <p>"Yes, lord..."</p>
  
  <p>"Potthapada, it's as if a man at a crossroads were to build a
  staircase for ascending to a palace, and other people were to say to
  him, 'Well, my good man, this palace for which you are building a
  staircase: do you know whether it's east, west, north, or south of
  here? Whether it's high, low, or in between?' and, when asked this, he
  would say, 'No.' Then they would say to him, 'So you don't know or see
  the palace for which you are building a staircase?' When asked this,
  he would say, 'Yes.'</p>
  
  <p>"So what do you think, Potthapada — when this is the case, don't the
  words of that man turn out to be unconvincing?"</p>
  
  <p>"Yes, lord..."</p>
  
  <p>"In the same way, there are some brahmans &amp; contemplatives with a
  doctrine &amp; view like this: 'After death, the self is exclusively happy
  and free from disease.'... Don't the words of those brahmans &amp;
  contemplatives turn out to be unconvincing?"</p>
  
  <p>"Yes, lord. When this is the case, the words of those brahmans &amp;
  contemplatives turn out to be unconvincing."</p>
</blockquote>

<p>, whilst Absolutes are not Absolutely denied by the Buddha, given the empirical evidence of impermanence (and the non-self that follows), the only place where such Absolutes could be found is beyond empirical evidence - beyond experience (or Metaphysics, 'after Physics' - as Aristotle stated, with regards to the investigation of 'things' beyond evidence). As such, this Essentialist Truth - whether theistic or nihilistic - is only ever an inferred Truth - never a directly perceived Truth.. Plato's Parmeneides says as much!</p>

<blockquote>
  <p>".......... Then the one does not exist in such way as to be one; for if it were
  and partook of being, it would already be; but if the argument is to
  be trusted, the one neither is nor is one? </p>
  
  <p>True.  But that which is not admits of no attribute or relation?  Of
  course not. Then there is no name, nor expression, nor perception,
  nor opinion, nor knowledge of it? </p>
  
  <p>Clearly not.  Then it is neither named, nor expressed, nor opined, nor
  known, nor does anything that is perceive it. </p>
  
  <p>So we must infer.  But can all this be true about the one?  I think
  not. </p>
  
  <p>Suppose, now, that we return once more to the original hypothesis....."</p>
</blockquote>

<p>(Plato gets to the same understanding that Truth must be placed beyond all perception, if it Is. But he chooses to stick with the inferred argument, rather than follow perception)</p>

<p>The Buddha's insight however, is to be fulfilled at its end, with perception alone, as demanded by the Kalama Sutta (<a href="http://www.accesstoinsight.org/tipitaka/an/an03/an03.065.than.html" rel="nofollow noreferrer">http://www.accesstoinsight.org/tipitaka/an/an03/an03.065.than.html</a>):</p>

<blockquote>
  <p>"Of course you are uncertain, Kalamas. Of course you are in doubt.
  When there are reasons for doubt, uncertainty is born. So in this
  case, Kalamas, don't go by reports, by legends, by traditions, by
  scripture, by logical conjecture, by inference, by analogies, by
  agreement through pondering views, by probability, or by the thought,
  'This contemplative is our teacher.' When you know for yourselves
  that, 'These qualities are unskillful; these qualities are
  blameworthy; these qualities are criticized by the wise; these
  qualities, when adopted &amp; carried out, lead to harm &amp; to suffering' —
  then you should abandon them."</p>
</blockquote>

<p>and as fulfilled by all that become Arahats, as did Sariputta, helpfully described by the Buddha in the Anupada Sutta (<a href="http://www.accesstoinsight.org/tipitaka/mn/mn.111.than.html" rel="nofollow noreferrer">http://www.accesstoinsight.org/tipitaka/mn/mn.111.than.html</a>).</p>

<p>In his first sermon (<a href="http://www.accesstoinsight.org/tipitaka/sn/sn56/sn56.011.than.html" rel="nofollow noreferrer">http://www.accesstoinsight.org/tipitaka/sn/sn56/sn56.011.than.html</a>) the Buddha stated the Four Noble Truths (<a href="http://www.accesstoinsight.org/ptf/dhamma/sacca/" rel="nofollow noreferrer">http://www.accesstoinsight.org/ptf/dhamma/sacca/</a>). These Truths are no thing more than declarative statements as to how the world is perceived to be. In a world that has Absolute constructs, the 'Truth' that 'all conditioned experience is suffering', is simply false. But no such world is either perceived to manifests empirically, or can be created within though without creating contradictions (for this read Nagarjuna's 'Fundamental Wisdom of the Middle Way').</p>

<p>The Buddha does link stress/suffering to impermanence and non-self within the Truths, and at this juncture you can definitely argue that psychology will play a part, as stress and suffering are psychological experiences, but you would have to find a mind that prefers constant change (and this includes death and rebirth) to certainty to argue that the Truths fail within the empirical world. </p>
