Ki Throw was in fact the feat I used as an example, but he decided that it is easier to throw somebody a distance than kick them, therefore an always-available feat ability is more powerful than a limited uses per day ability based solely on his own opinions.
Also, all rules that do not explicitly disadvantage the players to the benefit of GMPC's are subject to his knowledge of physics. He's studied a few years of Calc and Dynamics in his undergrad, so he fancies himself somewhat of an expert. Why that matters in a fantasy game is beyond me.
As for rerolling, I asked to do so the moment he said "4 Ki points", because I knew then and there it had nothing to do with balance and everything to do with arbitrating against a class he doesn't like, but he is not allowing rerolls. Probably going to just move on.
