So essentially you are offering condescension and obfuscation in lieu of argument.
(1) Native Americans clearly were not under the jurisdiction of the US because the US negotiated treaties with the various Native American tribes and nations as if these tribes and nations were external political entities.
Native Americans were under the jurisdiction of their tribes and nations in conformity to negotiated treaties.
(2) Unless the foreign national is in the US pursuant to some diplomatic arrangement, that person - be he legal or illegal - is under the full jurisidiction of the United States. He is obliged to obey US law or he can be punished with the full force of US law. An illegal Mexican immigrant or a French tourist cannot drunkenly run someone over with a car and claim that because he is a citizen of a foreign country he cannot be arrested, charged and convicted under US jurisidction.
Absence of owing any allegiance to any other foreign powerAnd talk about smokescreens! Suggesting that subject all foreign nationals except by prior arrangement full under the subject to the jurisdiction clause would render it a nullity. You (assuming you are a US citizen) are still subject to the jurisdiction of the United States while you are in Mexico. A Mexican citizen is not.
ML/NJ