I have not done the work of you, Evan, and others on this, but "subject to the jurisdiction" seems obviously meant to exclude those who refuse to be bound fully by our laws & whose refusal we accept, either because we choose to or because we must....
That makes sense of the use of both terms ("jurisdiction" in the text and "allegiance" in stray legislative history). To use it to refer to some imputed allegiance based on the visa status of one's parents engages in the precise kind of sophistry the language is trying DESPERATELY to forestall.
