His putative race does not really matter for my dislike of the term "race card", no you did not specify, but it is usually African-Americans who get that term used in discussions of race. However, if he is of a different race, all the rest of my post is still my feeling on the matter.
I myself have been involved in a case similar to this, and in no way did I feel like the student did not have the right to have his concerns answered, no matter what I might think of the circumstances. We work at institutions that have rules to prevent discrimination and students have a right see that they are enforced.
Were my feelings hurt, my time used in a way that I didn't foresee? Sure, but that's part of the job. It was also found to be untrue in my case, and I don't now feel like I need to document my every interaction with students of a different race as a result of the instance.
I also find "mental case" to be an objectionable term and hope it isn't a term you use in the classroom. I find part of being neutral as a classroom teacher is to not use loaded terms about people's characteristics and it's part of the code of the institution that employs me.
I do not believe that there is such an outbreak of accusations of racial bias by non-white students in universities that this needs to be discussed and warned against at length.
That is all that I have to say on this topic.