Just wanted to add my experience. National claimed I damaged a car in El Paso by damaging the underside of the front bumper . Talked with the National loss unit in Tulsa (that guy was easy to deal with, btw), who said they couldn't definitively prove I did it. In the end I let Chase handle it, even though I probably could have fought it more on my side.

Paperwork was a bit of a pain to gather, but in the end National sent everything they had to Chase and I sent my stuff over separately. Total time was three weeks before they cut National a check.

Easy to deal with, aside from the paperwork. I used Amex years ago and they were easy to deal with as well.