Does mutual exclusion hold in this case?
Your friend is correct. In your context, mutual exclusion holds if at most one process is at a critical section at any given time.

You state that you feel that this interpretation is wrong, but you have not been able to prove your intuition. You cannot prove a definition! What you are really saying is that the concept of mutual exclusion is vacuous if no process is ever in a critical section. To some extent you are correct&mdash;this agrees with colloquial usage. The same colloquial usage also states that "A or B" has the connotation of "A or B, but not both". When dealing with formal concepts you have to forgo the colloquial point of view, trading it with the mathematical point of view.