[PantsOnFire]

Here is the underlying reasoning for this sort of ruling.

Player A bets, Player C wants to call Player A. Player B in between them goes all-in but it is not a full legal raise. It is therefore treated as a call (under-raise if you will). So now Player C still wants to call so he puts in the identical amount that Player B did. Now Player A cannot raise.

Your buddy is correct to say that you can't raise an under-raise (since it is technically an oversized call). However, in your scenario, Player A is not facing an under-raise, he is facing a raise from Player B and a call of that raise from Player C. So he can in fact re-raise Player B.