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.
I heard on TV the other day, that the sponser of this amendment stated specifically that this amendment did not apply to illegal aliens. The INS just interprets it differently.
It seems to me that Congress can flesh out the definition of the term jurisdiction to state that such children are not considered under the jurisdiction of the USA for the purpose of citizenship.
The fact that people are under the jurisdiction of USA laws, does not always mean they are citizens. Indians for example, while subject to jurisdiction with respect to USA laws, were not considered citizens, as they were under the tribes jurisdiction with respect to that.
Congress can also propose a constitutional amendment, I really don't care which method is taken as long as it is taken.