To play the devils advocate, is it not the case the external thrusters are depleted during the atmospheric stage?
To my way of thinking if you had rocket gently orbiting and the entire combuster nozzle array were suspended by tensional springs attached to the body of the rocket itself and you fired the engine the whole array would tension forward on its support springs. Thus in turn dragging the body forward with it.
If this is in fact the case it would be proof postive that the thrust is a pushing force and not as the good professor claims simply thrust without push based on the 3rd law.