Good move getting the inspection. As I was reading your original post, I was about to respond with the suggestion that invest a few hundred of the cash compensation in a thorough examination.
What doesn't sound right to me is -- given how tough cutting through tires can be, there are other much easier ways of causing damage (convertible top, window, paint etc.). Did you ask to view the damaged tires? Does the mileage show anything unusual? Maybe I'm getting paranoid here