Be prepared to still end up paying something. In addition to repair costs, Hertz will likely charge for "loss of use" (the rental revenue they lost while the car was out for repair instead of being rented to someone), administrative fees (which are kind of BS) and in some states (not sure about NY) "diminished value" (because a car with a crash on its record will have a lower resale value than one with a clean Carfax). Depending on your insurance and Amex's policies, they may not cover all of those categories. I know (from experience, unfortunately) that Travelers and Chase won't cover diminished value, for example. That said, the number that Hertz first throws out is usually negotiable, and the folks at both your insurance company and Amex will likely negotiate it down a bit. So you probably won't end up paying more than a couple hundred dollars at most.