So perhaps you could explain the inclusion of this "extra" text in the Constitution?
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of PresidentML/NJ
Some of the Framers were not natural born to the colonies. James Wilson, Alexander Hamilton for example.
At one point in the Convention it was suggested that senators needed to be native born to be eligible. Wilson argued this was not fair to people like him as he was helping to write the Constitution but would be prohibited from being in the government it created.