A large amt of credit cards pay for damage below your insurance deductible - so that could come in helpful. But I'm sure before that even comes into play, Budget may note your thus far fight of the situation and decide not to pursue it. There are posts throughout the rental car forums of folks getting "dinged" for damages, them telling the first person who contacts them the story, and then never hearing from them again. You should be OK.

And should it, in the unlikley event, go further, and they play the "we lost use of the car x days and therefore you owe us revenue of..." ask them to document that they were sold out and had demand that day. They won't be able to prove it.