Babeu was on a helicopter tour of Mexican drug cartel scout locations in caves in the side of mountains throughout the desert about 70 miles inside the U.S. border. Essentially, that means U.S. sovereignty is gone for hundreds, perhaps thousands, of square miles throughout the American southwest.
And if the state or federal government were later to claim a child born within such an area was not a citizen and could establish that lack of jurisdictional control, then the claim might have merit. Though it would make for an odd role-reversal, with the U.S. side asserting it lacked control over a portion of its territory and the other side asserting "clearly it's U.S. land."
I suspect that the number of children born out in the desert wilderness is but a minuscule fraction compared to those born in urban areas and hospitals. The effort to prove the rare exception wouldn't be cost-effective.