I like the way you think.

It actually stood for Additional fuel
for delivery,meaning the vehicle got a full tank of gasoline upon delivery to the customer,especially if it was via train from the factory..Sometimes they would notate the cost as being paid by the dealership,but often times it was commingled in with the final total making the customer feel he got a freebee,when he really didn't.
Can you imagine how much this would cost dealerships today.