I can't be certain, but I think the issue is a slightly different one. (Basing this speculation on my 30 years in the insurance biz.)
Imagine for a moment that you borrow my car, and I agree that if you bang it up, I won't charge you anything. Now imagine also that someone else says that if you bang up my car, he'll pay the cost of the repairs. You could potentially gain by intentionally banging up my car.
I don't think it's necessarily a question of paperwork, more of making sure you can't gain by having an accident.