Question: 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?

Answer: 
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."
Advisors propose activities to students to give them opportunities: to learn, to build connections, and to become known in their field. All things that can be useful for the students' future careers (many of my current colleagues are actually people who I first met at a summer school). 

Thus, I would consider your friend's email offensive (and, *no*, I'm not a particularly polite person in everyday life).