The Founders spelled out the qualifications for President, in positive language rather than negative language.
Any President is required to be a Natural Born Citizen, which means that Naturalized Citizens do not qualify to be POTUS.
And in answer to your question, I think “subject to the jurisdiction thereof” can handle man of these other issues. For instance, I think the illegal alien “anchor baby” issue can be resolved by Congressional notice of the fact that no United States divorce court would have jurisdiction over custody of a couple's children, if the husband and wife were not citizens of the United States. Therefore, the child even if born here would not be fully “under the jurisdiction thereof” -— a few conservative members of Congress happen to agree with me on that point as well.
It does you no good to argue with the birthers. I’ve repeatedly asked them to identify any official document of any kind that differentiates beween a citizen by birth and a “Natural Born Citizen”. Of course they can’s point to anything.
“For instance, I think the illegal alien “anchor baby” issue can be resolved by Congressional notice of the fact that no United States divorce court would have jurisdiction over custody of a couple’s children, if the husband and wife were not citizens of the United States. Therefore, the child even if born here would not be fully “under the jurisdiction thereof” “
I agree with you on that point. Where would that leave the child of a couple just visiting the US? Would their child be a natural born citizen, then?