Whenever you pull someone from an executioner cage, it won't activate any unhooking related perks, and doesn't count toward challenges. I feel like it should at least count toward challenges, because you could unhook people 10 different times, and not get a single challenge done.
So I've noticed that if you do well enough, no one will be injured or anything. However, when this happens, your altruism badge is almost guaranteed to be nothing. I don't really think that's fair. There was no altruism to be done. Why take away from me when we did great? I think maybe if no one gets hurt or hooked or…