I am confused. I have not ever, ever, ever (is that enough?) had to enter my AAA # to book a Marriott AAA rate (or show the card, for that matter). Hilton yes to book, and once at a Holiday Inn Express at MUC they wanted to see the card, which of course I didn't have, but was able to log in to my account from the lobby public PC which satisfied the clerk.
And, I've never been asked to prove that I'm qualified for the Senior rate, which I am, but don't look it. The clerks probably feel sorry for whoever books that way.
I may have been asked for my corporate ID/business card twice over the decades.