I can't confirm anything, but logically I'd say that the issue is bigger than whether you have the correct back-up ID. If you are not part of the group that the AWD code contract covers (between Avis and an affinity group, say, or an employer) than the insurance coverage contracts may not cover you, even though they are included in the AWD rate for those who ARE legitimately covered and even though Avis has allowed you to get the benefit of the lower rate. The insurer (or Avis, or the employer, if it is a self-insure arrangement) probably has agreed only to cover renting employees/members of XXXX. You could try saying "Well, they gave me the rate, so I thought I got the insurance too," but I'd hate to be banking on winning that one.

Being risk-averse on this sort of thing, I do all my car rentals on a credit card that provides PRIMARY auto insurance coverage for rental cars (most that say they provide rental insurance are only secondary to your own insurance). That means I can't take advantage of AWD's requiring use of a different card, but at least I sleep a little better when renting a car!