Just need to clear up that subject to the jurisdiction of the USA does not include people who are here illegally. Their jurisdiction for the purposes of citizenship is the country for which their parents are citizens.
Jurisdiction is the practical authority granted to a formally constituted legal body or to a political leader to deal with and make pronouncements on legal matters and, by implication, to administer justice within a defined area of responsibility.
While immigrants (illegal and otherwise) are here, they ARE subject to the jurisdiction where they reside. When they are in Mexico, THEN they are subject to the jurisdiction of Mexico. I wish you were right, BUT you are not.