Assertion without argument is meaningless. Where exactly are you contending the logic fails? So far, I've not seen anyone anywhere give a definition and rationale for "subject to the jurisdiction thereof" that includes legal aliens while excluding illegal aliens.
Perhaps you can try.
your implying rules of law for legal aliens are somehow different than illegal aliens because of their status.
If you come into this country illegally, you should be tossed out- the fact that you drop a kid here should not give you immunity OR allow you to claim legal status for the child