While I am not an expert on auto insurance, I did review both the coverage on my auto policy (USAA) and my credit card (Amex).
On my auto insurance, I am covered for non-owned vehicles as long as I have a reasonable belief I am authorized to use the vehicle. Even if National says I am not eligible for the code, I still believe that I am authorized to rent the car, the only question is the price. As a result, I beleive my auto insurance would cover me, even if the damage waiver from National was not effective. But, I might have to pay an increase in the rental rate plus my deductible.
As to my credit card coverage, this specifically requires that I decline the waiver offered by the car rental company. As a result, I expect I would have no coverage from the standard coverage associated with my CC. So, again, I would have to pick up my deductible.
If I sign up for the AMEX Premium coverage mentioned in another post, the coverage is primary and pays without regard to declining the damage waiver offered by National. As a reuslt, this coverage should pick up the entire cost, including the deductible. Because I am a CA resident, this coverage is pretty cheap ($16). We may sign up for it.
Sorry this is so long, but everyone should remmeber that this discussion only relates to damage to the rental car (and its occupants), not to any other car or any other person. You need liability insurance to cover that and the potential claim could be huge.
While National's liability coverage is included with 57 and 67, if you have any concerns that your car insurance policy would not cover you for liability to third parties if you booked a reservation with these codes and were not eligible, you should think about booking only with a code that you are sure you are eligible for. That would probably also exclude the Carlson code, the Costco code is you are not a member, the Amex code if you are not a cardholder, etc.
Best of luck -- Suzanne