There is a huge distinction, however, between immigrants (legal and illegal) and Ambassadors. Ambassadors (and, to some extent, their families) often have diplomatic immunity - that is, they cannot be prosecuted for crimes committed in the U.S., and cannot otherwise be held liable by the U.S. for their conduct while here (though they can be expelled). They are the clearest example of people who are here, but who are most certainly not subject to the jurisdiction of the United States.
So, while it is arguable whether or not aliens are subject to the jurisdiction of the U.S., it is clear that Ambassadors are not - hence, it makes sense (at some level) to treat the situations differently.
My point is when interpreting the law, they skipped over the alien part.
The framers did not have a problem with immigrants, they were all immigrants, they did want allegiance. They did not want a free for all like it has become.