The only way the CC wont cover is if the rental was not legal. now, once the rental agency gave you the vehicle there's nothing illegal anymore, the rental is still legal they just didn't charge you the underage. But thats hertz' prob.
Is that an opinion?
It says black and white on the contract, that you represent that you are a member of the said CDP.
Fraudulent contract, possibly illegal, and therefore CC might not pay.