I always thought that if I rented a car from AVIS and used my Asiamiles card, then Asiamiles would be compensated in some way as a referral fee. I can't imagine Asiamiles paying Avis a fee for its members to collect miles in their own program.
My rule of thumb is: Whichever company receives money from customer pays a fee to the referrer (be it Asiamiles, Aeroplan, Mileage Plus etc.) The referrer then uses these proceeds to cover the costs of maintaining their ff program.