“that all persons born in the United States and not subject to some foreign power”
http://www.amnation.com/vfr/archives/008477.html
When an ordinary Mexican mom has just given birth in a Laredo hospital, there isn’t normally any Mexican official there able to exercise Mexican governmental power over the infant.
I can’t say the same for a wife of an ambassador, since the ambassador can pat the child on its posterior. The ambassador can tell any US official who walks in the room that the child has diplomatic immunity.
The issue is not territorial jurisdiction, it’s political jurisdiction which goes to allegiance.
The woman is a citizen of a foreign nation, i.e., a subject.
Therefore subject to the jurisdiction of the nation that she belongs to.
You are making the same semantic mistake that others do, because the original understanding is not understood now over a century and a half later. Eastman and Meese explain this in their brief in Hamdi.