Don't put 100 percent faith in carfax. When I was using it to check out a few vehicles, I decided to run a van I had at the time that I KNOW was in an accident, had an insurance claim filed, and repaired by a local shop. Nope, no record at all of it in carfax.
The unfortunate thing about Corvettes is that you can't use the age old trick of taking a magnet along with you to check for body putty on that car you are looking over.