I had to use CSP primary coverage to settle Avis' claim for $220 damage a couple of years ago. Yes, Card Benefit Services processed the claim. After contacting insurance rep I received a claim form to fill out and accompanying letter with the list of documents to provide. The list is below. They did settle the claim for me but not until I actually collected and provided every single document they requested.
If the rental was transacted on a company card (e.g. business, corporate, purchasing, or government):
▪ A letter from your employer stating that the rental was for business purposes
▪ If your rental was not used for business purposes at the time of the incident, follow the personal card instructions above
This is interesting. I thought the coverage would be voided if the rental was not used for business purposes. Apparently it would still be covered.