The problem with the AA is that they're set up to deal with the lowest common denominator - those that know nothing about their car, and like any big organisation it's difficult to deviate from the set process. They have to send a patrol first to assess, regardless of whether you know what the problem is and that they can't fix it by the roadside.
The only time I managed to get around this was when my V8 Merc shredded its aux belt, and I managed to get the patrol guy to pick up the right belt beforehand...did have to get rather insistent with the lady on the phone though.