The fact of being born on US soil does not automatically make the child a citizen. If it did there would be no need to add the "and subject to..." qualifier.
I didn't say it did. I'm saying *the child* is subject to the jurisdiction of the US, even if the parents are not. Only in those cases defined or international agreement with the parents country (or equivlaent multi-national agreement), is the child not "subject to the jurisdiction". The case of the Indian tribes is illustrative. Indian tribes were considered semi sovereign entities, and their members were not fully subject to the jurisdiction of the United States, they could not be drafted for example, until the law was changed to make it so. But the law cannot go the other direction, making some group not citizens who heretofore were, that would be a bill of attainder, which is prohibited by the Constitution. Naturalized citizens can individually have their citizenship revoked, for crimes committed or fraud during the naturalization procedure, but natural born citizens cannot. More's the pity as I can think of any number of citizens who richly deserve such a fate. Michael Moore, Alex Baldwin, and several others who promised to leave the country if certain events came to pass, but when they did, reneged on their promise.