More of an ethics question - is it okay for him to contend to have information on another doc's patient's health?
I don't see a problem with that as long as it's a false claim. If he's using that vague statement as a way to say "I saw her on TV and she looked a bit pale" and that's just his personal opinion and if listeners draw and inference between his personal opinion of a non-medical nature and the fact that he's a doctor, then that's the listener's mistake and not his responsibility.
If, however, he actually saw Clinton's medical records or overheard one of her doctors talking about them and then made that same vague statement, then he needs to lose his license and be sued into bankruptcy.