AAA WILL tow, it might be a matter of slipping the drive $20. They get called out tow all sorts of abandoned/unregistered vehicles all the time. They don't care all that much, they get paid by AAA, not the customer.

I used to party with a guy that would flatten a tire wherever we were drinking at, call AAA, get us and his car towed home. Cheaper then a cab, and all he did was refill his tire. The drivers really don't care all that much. They get paid either way.