The CM probably meant to say that there weren't any rooms available at the AAA rate or she was mistaken.
You can use AAA for a discount on AKL Concierge but only if there is a room available at that rate for the dates you need. The only have so many rooms set aside for AAA, AP, DC, etc.
You could keep checking but will probably end up paying full price if nothing opens up.
If this is for next June, they may not even have AAA rates out yet so just hold onto your ressie and check for a AAA rate when it gets closer to your trip. Also check out mousesavers.com for info on AP rates, codes, etc. You will see more info become available when it gets closer to next June.