quote "Plane is sat on the treadmill thingy, engines off. Treadmill starts up - the plane will start moving backwards with it, right? I think we can all agree on that. "
not necessarily true, this is all down to the friction of the wheel and the hub. In previous examples when people say that they are holding the plane/cyclist/ matchbox car still on the treadmill they would only be exerting a force on the object equal to the friction forces of the object on the belt. If a brick is on the treadmill then it would move at the same speed as the belt. A tennis ball would spin and move along at a lower speed than the brick
If you had a rug with a ball on it and pulled it slowly the ball would move with the rug as the friction force holding the ball would stop it moving, if you pulled the rug fast the ball would spin back and not move as fast