People elsewhere on the flist have reported that physical activity requiring high dexterity and mental focus helped them cope with PTSD (horse riding, martial arts) so it's not an obviously stupid decision. It would probably be ill-advised if there were existing signs of violent impulses, but that can be very hard to anticipate.

(I get a sense here of LOLing about tragic deaths, and assumptions that mentally ill people must be violent, that don't become sympathetic just because the victims may or may not have been right-wing)