Typically, car was damage is to the wipers and antennas. Pulling off a bumper requires rather a lot more umph than a piece of wet rag hitting the car, can give.

I'd guess they really do have footage of you driving in, with a damaged bumper. I'd guess, whereever you parked it before that, someone hit you while parked.

You can always sue them. But you're probably going to lose, all they need to do is bring that footage to court. You can also file the claim with your car insurance, if you have collision – and then try to get your insurance to chase them down, but if they show the insurance their proof, that's the end of it.