1) those children born overseas and who come with their immigrant parents to this country, and
2) those children born in the U.S. to immigrants, whether or not the immigrant parents ever become naturalized citizens themselves.
Those in category 1) formerly became naturalized when their parents became naturalized, now they have to apply separately. Those in category 2 have always been natural born Americans. At any rate, that's how the American government has been applying the law for about, oh, 235 years.
Remember to always get your legal advice from some anonymous blog on the internet. Never, ever, ever go to a legal expert who might actually know what the law is. The government relies on its own legal experts, which of course is why the government's wrong.
Married women, and children under the age of twenty-one, derived citizenship from their husband or father respectively. Children of unsuccessful applicants could apply for citizenship in their own right, at the age of twenty-one.
(an American woman who married an alien lost her U.S. citizenship, even if she never left the United States.)
Under US common law, children born on US soil, even if the mother was a US citizen prior to marriage, did NOT automatically gain US citizenship & especially ‘natural born’ US citizenship.