The AA know that they do get ripped off, a lot, by people (minicab firms, usually) who take out one "personal membership" - entitling the member to call them for breakdown repair / relay etc, whatever car they are in, even if they are a passenger in a friend's car.
The cab firm then proceed to use this one membership whenever any of their fleet of cars breaks down.
Each cab driver who's car breaks down then pretends that he is the guy whose name the AA membership is in, but says that he's not got his membership card on him.
This is probably why they might want to check if someone actually is the person who has paid for their breakdown cover.
Giles..
PS - if you've made quite a few call-outs to them in the last few months, I can imagine them being more suspicious.
You don't have to actually have your membership card on you with AA, but don't most people have something with their name on it, in their pocket, when out and about? ATM card / credit card? Driving licence? Work ID?