If you feel like Uber is trying to screw you over, I would get a lawyer and not talk to anyone else without your lawyer present. The last thing you want is for Uber to not cover it and throw you under the bus. It sounds like you did everything correctly and shouldn't be held accountable for someone else actions which led to them hurting themselves. Especially if you have video, it will show that you are not liable and didn't commit any actions which led to the pax being hurt. Hope everything works out for you.