Huh. My (mainland Chinese) wife told me about this story after reading about it in the Chinese press. I thought it was sensationalized a bit, but this article lines up with what she told me pretty well (though maybe that just means the AP is sourcing the Chinese press in its article).

Apparently a lot of better-off Chinese women travel to the US to have their children, though they don't stay there, so they're not technically "anchor babies." Still, given the prevalence that it happens, I'm surprised I've heard so little about it in the US press, especially given how the citizenship-at-birth issue has been debated recently. And apparently this particular woman's other children were also born in the US in the same manner…