Originally Posted by Beckles

OP, it's not clear in your intial post if you did this or not, if you have your own auto insurance collision policy you need to file a claim with them unless your credit card provides primary rental car coverage (which is not typical, the two biggest exceptions being Diners Club cards and the supplemental AMEX insurance where you pay a per rental fee).
A rental car company does not have to prove they had every car rented to be entitled to loss of use.