Was Grandma A Native Born Alien?

In the United States, during the time before the Cable Act, a native born American woman would lose her citizenship status if she married a man who was an alien. This explains why the 1920 census for my children's great-great-grandmother indicated she was an alien even though she was born in New York State. Her husband was an unnaturalized Greek immigrant.

Did your female ancestor lose her citizenship because her husband was an alien?