Okay, this is completely permissible through the fourteenth amendment. Whether you are here legally (like these Chinese visitors) or illegally, you are under the jurisdiction of the United States. As long as you are within the U.S. jurisdiction and you have a child here, that child will be naturalized. This goes for illegal immigrants too. For once they are found here illegally, guess what? They are under the United States jurisdiction at that point. That's why a constitutional amendment to not give naturalization to a child of an illegal immigrant does not make sense. Once they are born, they are just as American as the rest of us... Think about it.
Born In The U.S.A.? Some Chinese Plan It That Way : NPR