Right - so check with your own company. Here's a simple statement from mine, which is also in the US "Car rentals must be charged in full to the Card, cannot exceed 48 consecutive days and the rental agency's Collision Damage Waiver must be waived by the Primary Cardholder." On the phone, they said that you must pay for the rental with the card (to an agency or the company) and when you are asked if you want the CDW when you take the car you must decline. Seems that it would be unreasonable to demand that you cannot have paid Priceline if what you are purchasing is a car rental. But you can't assume - so ask.
I found most US issued MC or VISA CCs that have CDW limit it to 14 days max (at least those CCs that I have/had) a Biz CC usually 30 days.
To get around that 1 has to return the car and rent either the next day or go to another rental company. Was told back to back contracts even if with a return and then a new rental contract is a no-go on the sameday from the same outfit, doesnt make sense but Id hate to be stuck with having to pay out of my pocket for the Repairs