Not true at all.
1883, Secretary of State Frelinghuysen determined that a man applying for a U.S. passport, though born in the U.S., was not born a U.S. citizen because he was subject to a foreign power at birth having been born to a non-citizen father.
1885, Secretary of State Bayard determined that the son of a German subject, born in Ohio, was not a citizen under the statute or the Constitution, because he was on his birth subject to a foreign power, and not subject to the jurisdiction of the United States
Any examples in the 20th century?