AA says OK ... Avis says No Way ... oh let's just call the whole thing off!

Avis consistently says we can get the multi-thousand-mile bonus only once; AA says we get it as many times as we rent a car. Who will eventually decide if we get our bonus? Avis, because they must be paying AA for the miles, or AA because they were the ones who introduced the promotion?

I think it's not worth going too far out of the way to use this promotion, since it looks like it will be uncertain (after the first rental) if we can get the bonus. Does anyone really know?