Incorrect. One side has legal support, one doesn't.
"To me, the key is the phrase, " . . . subject to the jurisdiction thereof . . ."
Thank you Captain Obvious. :-)
"What about fugitives from justice? Have they rejected the jurisdiction of the US, and not be ''under' that jurisdiction since they are fugitives?"
No. You can't "reject" jurisdiction. It's not up to you.
If you are not "under the jurisdiction" then you are not subject to the law.
"I'm not going to provide my own opinion on that question, except to say that the answer is not black and white. It is subject to interpretation."
Actually it is black and white. Just read the Wong decision, it's pretty much laid out. Those not "under the jurisdiction" are diplomats with diplomatic immunity, invading soldiers operating under the laws of war, and Indians on sovereign indian territory. What these all have in common is that they are not subject to US law. Everyone else is.