If all "subject to the jurisdiction thereof" meant was that the United States had issued them a visa, it's over.
If this issue goes to the Supreme Court you can be 100% sure Sotomayor, the Wise Latina, will answer YES to the above question.
AS usual, it will be a 5-4 decision ( assuming we have the same people in the SCOTUS ), with Kennedy giving the deciding vote ( depending on which side of the bed he wakws up in the morning ).