If you use the debit card, why not simply pay down the credit card with the same funds you'd use for the car and then charge the car to the credit card? You'd get the credit card cash back/bonus points/etc, have the rental on the credit card in case something happens (secondary insurance coverage, dispute resolution, separation from bank account in case of skimming), pays down the balance (even if temporarily)and make your card issuer happy you are using them.