I believe Trinity is referring to the concept of non-citizens coming to the United States, and giving birth to a baby while here. According to the Constitution (14th amendment), anyone born in the U.S. is a citizen.
Given that Constitutional rule, there is at least the possibility that people come here (illegally, or legally) in order to have a U.S. citizen baby. This baby is then an "anchor." If the non-citizen parents would like to live in the U.S., they can appeal to the fact that their baby has a constitutional right to stay, coupled with the sentiment against splitting up the family.
I don't see that the term "fallacy" applies because it is at least a theoretical possibility, and it entails no contradictions. The real issues include: how often does this occur? what problems (if any) does this cause? If it's truly a problem, what can we do about it?