Is the phrase "thanks, but no thanks" appropriate in an email sent to a supervisor? I recently have had a discussion about my friend's tone in his email.

His supervisor asked him whether he wants to attend a summer school in May. He wanted to thank him for his invitation and also wanted to keep the mail short. As a result, that is what he came up with:


  Hello Professor,
  
  I have plans during that period. Thanks, but no thanks.
  
  Regards,
  John 


He is getting along well with his supervisor, but I believe that the phrasing is a bit disrespectful nevertheless. It might be the case that I am not a native speaker. 

Am I exaggerating the situation and this is something can be overlooked?
It sounds extremely rude, I am afraid. I would assume mitigating circumstances for a non-native speaker, but the "no thanks" permits "thanks" to be interpreted as substantive, and thus has a highly dismissive connotation which should never be used with your superior, and neither with a friend you would like to keep.

The connotation that shines through (at least in the UK) is a sarcastic "Yeah right, you think you do me a favour? In future, please spare me your ideas."