I am not saying that the valet company should not pay for anything. In fact, the valet company should pay for everything per OP.

However, National does not care who or which is responsible. As soon as OP's name is on the rental contract and CDW is not included, National will go after OP unless someone (OP or not) to pay up.

IMHO - once National has the final bill drawn, OP should demand the same amount from the valet company and the amount should be payable to OP. OP then will pay National. It sounds complicated. But it can ensure that OP will not be caught between National and the valet company.