relevant muscle activation

Obviously they play a part in stabilising the arm to an extent, but any serious activation would impede the triceps (a real player in the bench press). I've never heard of anyone mentioning the bi's in terms of benching. Are you sure he's not meaning triceps, but got confused?

OK I've had a look about & found this (it's a pdf so you need acrobat to read it).
I'll now have to hold up my hands. I'd not seen this research, but basically yes the biceps are more involved in benching than I expected, again I'm not certain how it can do much more than stabilise, but maybe the stability factor of the lift puts more on the biceps than at least I suspected, so technically yep, it will 'work' the biceps to an extent, but even so I still find it hard to suggest it as a 'main' player in the move, it's function has to be to stabilise, not pull (yes you can & do work your abs using stability but biceps aren't the same thing).
I think it might be an issue your mates going to have to 'play nice' with, nod his head & answer the exam question like they want, then forget about it.
That'd be my advice.

The idea might be it's like one of those 'trick' questions, so the teacher is preparing. Also stabilisation is more than balance, it's holding the elbow (& probably more importantly in this case) the shoulder (glenohumeral joint) stable. I mean in terms of exercise stimulus I believe your friend is right, but in terms of medical accuracy the trainer is right. As I said he probably needs to remember it for the exam, but then forget it as a relevant fact (except of course in injury/rehab situations where again it might be important)