My better argument is to include what the Supreme court said BEFORE that quote I excerpted.
Every person born in the United States, and subject to the jurisdiction thereof, becomes at once a citizen of the United States, and needs no naturalization. A person born out of the jurisdiction of the United States can only become a citizen by being naturalized, ...
I read it as the Supreme court declaring that "Jurisdiction" means within the actual borders.
You are trying to redefine the word “jurisdiction”. Nice try though. Does the US Govt have Jurisdiction over soldiers in battle in Afghanistan or Korea or Germany?