I don't think so. If you read Priceline's terms, they pretty much spell out that car rental companies have these policies.

Your husband wasn't denied the rental because you paid for it on Priceline.

Your husband was denied the rental because he didn't have a Credit Card...any Credit Card...to fulfill the additional requirements of the car rental agency. And Priceline basically warns you about that in advance.

That being said, Priceline has been known to make rare exceptions (minus a fee) if they can manage to get your money back from the car rental agency. But that's up to the car rental agency, and they don't have to as they were willing to provide the car if you were able to fulfill their normal requirements (valid drivers license, good driving record, credit card in name of contract/driver etc.)

You'll have to follow the links on Priceline to find the number to call to start the process. But I think you've got a tough one ahead of you.