But why are you assuming that the parents aren't US citizens? I got the opposite impression, that they probably are. And for that, the location of the child's birth has literally no bearing on citizenship. It would only matter if the parents were in the US temporarily or (I think) permanent residents but not naturalized citizens.

Like I used to live in El Paso, and I used to pop over the border pretty regularly. If I happened to be pregnant and went into labor unexpectedly on a shopping trip in Juarez and wound up giving birth in a Mexican hospital, my kid would still be a US citizen, because I'm a US citizen. I actually did know a few US citizens with strong ties to Mexico who chose to give birth down there for various reasons (often to be with family), and their kids were still citizens.

Pretty much the only time the birth location should matter is if the parents are not US citizens. Otherwise, you might have to jump through a few extra hoops to get a US birth certificate for your kid, but your kid is still a citizen no matter where in the world they were born.