Nothing in your posts (so far) indicates that MasterCard is requiring that one use the card to reserve the rental car (especially if the car-rental company does not even take credit-card information when a reservation is made).

You might want to ask MasterCard whether they extend the loss/collision coverage to car rentals obtained through Priceline or Hotwire, if a MasterCard is used. If their answer is yes, then I would ask them how your situation is different. I believe that the car-rental companies treat Priceline/Hotwire reservations as prepaids, and, in any event, the customer is making a credit-card payment directly to Priceline/Hotwire, and not to the car-rental company.