I don’t read it that way, nor do a lot of people.
"All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."
The problem is some people want to read a meaning into "under the jurisdiction" that isn't there. If you are under the jurisdiction, you are subject to the law. Think about who that applies to, and who it doesn't. There are very few categories of people who are not subject to our law while on our territory.