No, you are mistaken.
A person who is born here to parents who are foreign nationals residing here legally is considered a native born citizen, but can be registered as a citizen of his/her parents nationality. President Barack Obama’s father was a British citizen and registered his son as a British citizen and later as a Kenyan citizen. Whether born in Hawaii or not, he is NOT a natural born Citizen.
“A Natural Born Citizen is born to two U.S. Citizens on U.S. soil.”
See: http://www.naturalborncitizen.org/
and: http://naturalborncitizen.wordpress.com/
The explicit description for “native born citizen” has been spelled out in case law. Suggest you query for “Wong Kim Ark”, a SCOTUS case that delineated native born citizen. Nowhere in that case is a person born in the U.S.A. of foreign parents EVER described as a natural born citizen.
I have read Wong Kim Ark. It held that the plaintiff, who was born in California to two alien Chinese parents, was a natural-born citizen.