From what I have heard, and I have not checked this out officially, but if you put your car on a track, you are no longer insured. Insurance only covers the car on public roads as far as I know.
As everyone has probably already thought, the guy in the Z06 should have put it in Competitive mode and kept his active handling on as it would have caught this type of thing and most likely saved the car. Good thing that Camaro is fast.