he'd go as far as to manipulate this girl (who's name Ive forgotten) into becoming his murderous pawn.
That girl was messed up from the start, so he used her, it's like use bad guys to kill another bad guys.
So yes, he will "go slap a student out of nowhere".
That quote used for killing, meaning the Prez won't kill someone just because someone break one law.
Example, that bully Satsuki death threat at Early Chapter, Prez wasn't planning to kill her when she first bully someone, he stated that he gave her a warning twice before.
Second, Akari. He could've killed her when she first breaking the law, usually fighting problem. But no, first thing he did was knowing of why Akari act like that, just like Satsuki.