There are other variables to consider when changing a flat tire on a car vs a bike. First, are you on a busy freeway with a narrow shoulder? Are you on an incline where the car might shift? Are you a woman in a high crime rate area? Are you elderly or disabled and do not have the upper body strength to torque or un-torque a lug? In those instances AAA makes sense.
However, most bicyclists, if motivated and trained, can swap a tube.