If you want to keep your rate, all you have to do is write a letter stating you would like the AAA agent to take over your reservation. I have done this in the past. It did not require me losing my discounted rate and have to take the AAA rate (which would have been less off/cost more).
HOWEVER....
the key is to use an EXPERIENCED Disney AAA agent. And that would not be the one you talked to as she did not know how to do this.
I used a AAA agent that is well versed in Disney bookings and that is why it worked. Had I just called up a local AAA agent, I am certain I would have gotten the same response you did.
The benefits of booking through a AAA agent include the AAA parking pass (to park closer if it is avaialable), AAA discount at certain restaurants and shopping at World of Disney, and the storytelling experience at the Magic Kingdom (reserved time to hear a story read by a Disney character). Those are the ones I can think of now.
Hope that helps.