I accept the very reasonable presumption that Priceline's payment to the rental car company is not your DC. (If it were, Priceline couldn't make a profit!)

The fact remains that DC has earned essentially the same merchant discount from your Priceline charge as DC would have earned on the amount Priceline paid the rental car company. In my opinion, DC has no principled financial reason to exclude Priceline rental coverage.

Futhermore, if the terms do not spell out what happens for opaque bookings, I would expect any cardholder who challenges a denial of coverage to win.