I very much doubt that National would have put you on its DNR list if you had forwarded National's bill to you insurer for payment. Assuming that you had submitted all of the other required documentation for your claim, I expect that MasterCard's insurer would have paid the claim promptly.

Is your residence in NJ? NY? Someplace else? If NY, be aware that NY-issued non-owner policies automatically include rental-car damage coverage (to be paid out of the property-damage coverage on your policy). Because of that, only a credit card that offers primary rental-car coverage would be useful if you have a NY-issued non-owner policy.

Edited to add: Also, did this rental originate in NJ, or someplace else? Different states have different rules about what charges a rental-car company can collect in the event of an accident.