No, he doesn't. I know his is the position taken by the courts but it bears only the faintest resemblance to reality.
If you say illegal aliens are not under our jurisdiction, how can we prosecute them for illegal entry, or for crimes they commit while here?
Poppycock. If an Australian couple come here on holiday and break a law, they are subject to prosecution and deportation. If they have a child... they would not expect that their child is suddenly an American rather than an Australian. Only those who are coming here permanently seem to think it should work this way.
Back when Hong Kong was in the process of moving from British to Chinese sovereignty there were Hong Kong women coming to the U.S. specifically to give birth here, and then returning to Hong Kong with their new child. Why? So the child would have the option of claiming American citizenship if they would need it someday.
Will any of these children show up on our doorstep and demand to be let in? Probably some, not all. They are American citizens if they want to exercise that right.
This whole thread is about passing laws that will stop this, because the present laws don't stop these situations.