I understand perfectly that the engines thrust is independent from the ground, but they got it wrong, when he took his hand and pushed the car, the wheels were traveling faster than the treadmill.
In reality if he pushed that car and the wheels sped up, the treadmill would match instantly, forcing the wheels to speed up, which the treadmill would match... On and on, they would compound each others speed in an instant... If the treadmill had no limit to speed, it would be like splitting an atom, a uncontrollable chain reaction.