All they would need to do is threaten to stop sending any of a thousand essential commodities that make life tolerable (never mind what makes it possible), and any resistance collapses instantly. Mars colonists would be more directly under the thumb of Earth government than anybody outside of prison, an antarctic base, or navy ship.
I imagine the GP included "in the long run" to refer to a hypothetical future where the colony were truly self-sufficient (so able to produce any good that they want or need).
Exactly! This is why it eventually would need to become produced locally.
It's not entirely unlike an overseas colony in an inhospitable but not empty place. Start small and dependent, develop the land around you and become autonomous.
