you can only do this if the surface of the treadmill is an inertial reference frame. ie. a person running at constant speed vs a person on a treadmill at constant speed is functionally equivalent.

However, the moment you want to stop or change speed this no longer works - in the real world your body needs to accelerate, while on the treadmill the treadmill accelerates and your body does not. This is because the ground remains an inertial reference frame during the acceleration, while the treadmill surface does not.