First off, what the rep said was a load of BS. The AAA members do not need to be from the same state. As long as the primary renter and the additional driver are both AAA members, then there is no additional driver fee. Membership in AAA anywhere in the US is valid.
And yes, it is true that the primary renter and the additional driver both do need to be AAA members. Enforcement of this requirement is extremely spotty, but the terms do state both must be a member.