While I do agree that he shouldn't drop him, if he does then he does. For too long we have required a strong manager with standards. If this breaks one of Clements standards that he has set then he should drop him.
For example, Alex Ferguson was no stranger to binning top players who aired dirty linen in public. Walter wouldn't have wanted this type of thing either.
So it depends. It could be that Clement is OK with it. But if he isn't then it's the managers call to make. As it should always be around the club.