I just want to add, if 10th Planet kicked out people because they had mental issues, our moon(and probably most fight gyms) would be empty... But nobody is in any way a danger or problem for each other, or dis conductive to the training environment, and that's the important factor.
More than anything though, especially in martial arts, a person should not ignore intuition -- if something tells you something is off or wrong about a situation, it is, even if you can't point out what. If you were to ask someone to leave, it would be best to confront them directly on the issue, but with a rhetoric they can understand why or not be offended which can be quite the difficult task especially if they have a large ego/defense complex.
It sounds like you made the right move calling his parents, and you were right to be concerned in the first place. Chances are now the situation will workout for everything, and you'll be able to provide him with extra comfort in understanding of his situation. I think jitsu is therapy for ALOT of us, and has done alot of good for our minds being balance the distresses and conflicts we come across in life.