I thought it was more about if a foreign nation say, invaded and controlled a state, then we wouldn't be granting citizenship while it was under a foreign power.

Either way, no reading of that would apply to what the administration wants to see. I believe the argument I saw them attempting was to imagine another word was intended, "exclusively subject to the jurisdiction", meaning an otherwise stateless child becomes a citizen, but if they have birthright citizenship claim anywhere else, that is what the administration would want to use as an excuse to deny citizenship.