I think as long as someone who is staying in the room has AAA, that is fine. I have taken two trips with my boyfriend to WDW using the AAA rate. Once I booked room only with Disney and when we checked in, they didn't care that I was the one with the AAA card while the reservation was in my boyfriend's name. And at the AAA office when we booked a package, the AAA agent didn't care about that either. They both said as long as a AAA member is staying in the room, that's fine.
So I think as long as your Grandfather is staying in the room with you, then you can use his AAA card for the discount. If not, then no.