[ابو بيشو]

This is how I understand it too. In "You have a car" the "have" is not an auxiliary verb but a verb with the same force as any other (such as "drive" in "you drive a car, don't you?") and so the "do" tag form sounds correct to me. I think there is a vestige of an older usage in the way you can say "you have a car, haven't you?" (a time when you could even say "drive you not? etc"?) but it sounds very quaint to my ears.