If you were born in Mexico could you have a USA birth certif?

know this guy, he's kind of a fibber and just wanted to check out a story, said he was born in mexico and grew up there till 15 years old but has a usa birth certif, is this possible and also has a social security card, says when he was in the army (believe another tale) he obtained this birth certif ...just checking on this because he stays with my family also and just not sure why this would be made up etc ty