What does that phrase mean to you? At first blush, it just looks like the person is subject to the laws of the country.
There is Transitory Jurisdiction and there is Sovereign Jurisdiction.
While you or I are in Mexico, Mexico has a Transitory Jurisdiction over us, but the US has Sovereign Jurisdiction.
It is the NATURE of that Jurisdiction that tells the tale.
While Illegal Aliens are on US soil we have Transitory Jurisdiction over them for purposes of law enforcement.
But their country-of-origin still has Sovereign Jurisdiction over them.
Between the original intent of the 14th being to ensure that the children of slaves automatically became US citizens, and the abuse of the 14th as a Loophole for Birth Tourism and Birth Trespassing, and the dual nature of Jurisdiction, and given the size of the Invasion...
It will be convenient for the courts to eventually land on the side of caution and stick to the Original Intent of the 14th as a limitation.
And, while that may very well strike you as a "stretch"...
It would merely be using one Loophole (the nature of the jurisdiction) as an excuse and convenience to close ANOTHER Loophole.
Personally, I'm totally OK with that particular application, if the courts end-up leaning on that.