I think punctures are determined not only by damage model, but by set of tires. I've gotton punctures on lap 2 of practice, after doing a lap and a half at maybe 80% to feel out the track, on primes.
But, I can drive all out, get off line a bunch of times, and usually never get a puncture in a race, unless I do something drastic, or get wing-clipped on the wheel by someone.