I’ve been reading up on the 14th - another nod to The Donald for making me a more educated person. You are right - there is a clause within it that makes it quite obvious that to claim citizenship the baby’s parents must have ties within the United States and not from without. Slaves being the obvious example. Of course, what do liberal judges say?
There were a few 19th century court cases that confirmed the original interpretation until US. v. Wong Kim Ark, in which the SCOTUS said that a child of a permanent resident was "subject to the jurisdiction of the United States" of which Chief Justice Fuller's dissent is a worthy read.
BTW, that case for the original interpretation is made here.