(Congress shall have the power)...To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
Article II, Section 1
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 President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
Thank your for posting that. It explicitly states that congress may "naturalize" (meaning to make "like natural") someone into a citizen. This makes the distinction between making something "like natural" and what is already natural, much easier to see.
A "Natural" citizen requires no act of congress to be a citizen.
I agree that it says only a natural born citizen is eligible to the presidency, however, Article 1 section 8 and Article 14, section 5, both give Congress the authority to write the law about what constitutes being a natural born citizen.