I am having trouble wrapping my head around this scenario since in any case if the mine hex is controlled by an opponent the movement ends there and battle ensues
Well, if the mine hex is controlled by an enemy worker, you may retake it without a battle if your character or mech goes into the hex. You must stop that unit's movement, but if you have a second unit to move, they could then use the mine. Of course, you would now have control of your mine again, so the clarification doesn't apply, but a battle does not necessarily have to ensue.
If your mine is controlled by an enemy mech or character, then your mech or character must stop movement there and you don't yet control your mine.
Unless it only pertains to the mine as an exit once you have entered from a tunnel.
That is probably what the rulebook is trying to explain.