You may be right.
There are 2 terms to consider.
A natural born citizen refers to someone who was a U.S. citizen at birth, and did not need to go through a naturalization proceeding later in life. Under the 14th Amendment's Naturalization Clause and the Supreme Court case of United States v. Wong Kim Ark, 169 US. 649, anyone born on U.S. soil and subject to its jurisdiction is a natural born citizen, regardless of parental citizenship.
Then we have this clause:
Natural born citizens have all the same privileges and responsibilities as other U.S. citizens except for U.S. presidential eligibility. To become the President or Vice President of the United States, a person must be a natural born citizen. This "Natural Born Citizen Clause" is located in Section 1 of Article 2 of the United States Constitution.
Emphasis is mine, the full article may be found here: https://www.law.cornell.edu/wex/natural_born_citizen