Q:

Flaw in all scientific studies/experiments?

If you draw conclusions in your study based on reasoning like this paragraph below, it's automatically flawed, is it not?

"At the end, we compare the average energy levels of the two groups
  based on the observational study even if we find the difference
  between the average energy levels of these two groups of people, we
  can't attribute this difference solely to working out.
Because there may be other variables that we didn't control for in
  this study, that contribute to the observed difference. For example,
  people who are in better shape might be more likely to regularly work
  out and also have higher energy levels.
However, in the experiment, such variables that might also
  contribute to the outcome are likely equally represented in the two
  groups due to the random assignment. Therefore, if we find a
  difference between the two averages, we can indeed make a causal
  statement attributing this difference to working out. "

The paragraph says you can make a causal conclusion because of random assignment:
"such variables that might also contribute to the outcome are likely equally represented in the two groups due to the random assignment"
but that isn't guaranteed. Random means you could have, by chance, ended up selecting only participants, or a large majority of patients that have higher energy levels to start with..
So, is this just a really bad hypothetical example, or are all science experiments just as flawed as this one because they believe random assignment fixes everything?
I realize that the paragraph might need the rest of the context for anyone to really judge what I'm talking about, it's from 
https://www.coursera.org/learn/probability-intro/lecture/Qw8iF/observational-studies-experiments
and, the entire study is described here:

In an observational study, researchers collect data in a way that does not directly interfere with how the data arise. In other words,
  they merely observe. And based on observational studies, we can only
  establish an association. In other words, correlation between the
  explanatory and the response variables. If an observational study uses
  data from the past, it's called a retrospective study. Whereas if data
  are collected throughout the study, it's called prospective. In an
  experiments on the other hand, researchers randomly assign subjects to
  treatments and can, therefore, establish causal connections between
  the explanatory and response variables.
Let's pause for a moment to clarify what we mean by random assignment
  with an example, suppose we want to evaluate the relationship between
  regularly working out and energy level. We can design this study as an
  observational study or an experiment. In an observational study, we
  sampled two types of people from the population. Those who choose to
  work out and those who don't, then find the average energy level for
  the two groups of people and compare. On the other hand, in an
  experiment, we sample a group of people from the population, then we
  randomly assign these people into two groups. Those who will regularly
  work out through the course of the stud and those who will not. The
  difference is that the decision of whether to work out or not is not
  left up to the subjects as in the observational study, but is instead
  imposed by the researcher. 
At the end, we compare the average energy levels of the two groups
  based on the observational study even if we find the difference
  between the average energy levels of these two groups of people, we
  can't attribute this difference solely to working out. Because there
  may be other variables that we didn't control for in this study, that
  contribute to the observed difference. For example, people who are in
  better shape might be more likely to regularly work out and also have
  higher energy levels.
However, in the experiment, such variables that might also contribute
  to the outcome are likely equally represented in the two groups due to
  the random assignment. Therefore, if we find a difference between the
  two averages, we can indeed make a colossal statement attributing this
  difference to working out.

My entire point being:

A:

The reasoning in the first text is not flawed. It is correct.
Theory of random assignment
If treatment is randomly assigned, any unobservables in the treatment group will be balanced with unobservables in the control group. The same effects from unobservables in the treatment group will also be present in the control group! The difference in effect size between the two groups will be an estimate of the treatment effect.
The key concept here is that you don't need to control for everything to produce consistent estimates of an effect. You need treatment to be orthogonal of confounding, unobservable variables.
Can spurious things happen with small populations?
With small groups, you may, by chance have an unbalanced assignment of unobservables. Randomly pick a group of 10 people and you might have 7 guys and 3 girls. 
But if you randomly pick a group of 10,000, the split will be close to 50-50 (or whatever the split is in the population.) With larger populations, it becomes less and less likely that your control group differs from your treatment group by chance.
This may be a problem for small studies, but as they get larger, this is less of a concern.
The bigger problem?
In the social setting, you have many problems where random assignment may diverge from a mathematical ideal. For example, there may be selection bias.
Example:
100 kids are randomly accepted to a preschool program. Another 100 kids are randomly denied. It looks like random assignment of treatment (and a control group), but what if parents of the 100 kids that are denied INSTEAD find alternatives to the preschool program?
Denial of treatment causes kids to get unobserved, supplemental education! And unobservables aren't equally balanced between treatment and control. In some sense everybody got treatment! Your experiment then isn't comparing apples to no apples, it's comparing one kind of apple to another...
In the example in your question, I would think assigning people to work out may be quite hard! Does the treatment group actually work out? How do you prevent the control group from not working out? 
Summary
Do additional experiments help? Yes. They may use better techniques, have different error etc... More knowledge is better.
Can we have an unrepresentative control and treatment group by chance? Yes. But with true random assignment, it becomes increasingly unlikely as $n$ increases. Flipping coins, 47 or fewer heads in a sample of 100 is quite likely. 4700 or fewer heads in a sample of 10000 is close to impossible.
Should I trust my intuition on probability? Probably not. People (me included) have awful intuition about probability. It's hard.
So all science is wonderful? No! There are so many ways things can be wrong. Assumptions of the statistics can be horribly violated in so many different. Courses, series of courses are devoted to experimental methods for good reason! In practice, random assignment doesn't work as nicely with people as it does in the laboratory because people are clever, smart and can respond in ways you didn't even imagine! 

