“Both parents must be American citizens.”
Nope. Neither one has to be, birth on American soil is enough, or if born on foreign soil one American parent is enough. That is why Obama is President. Also why Jindhal, Rubio, and Cruz are (probably) running for President.
Birth on American soil makes them a citizen....but a "Natural Born Citizen" is something else entirely different. That's why the Constitution grandfathered part of the requirements of Article II; Section I which states
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.
I highlighted the part that no longer applies....namely a citizen of the United States.
You describe basically the requirements for citizenship not natural born citizenship. Different things. Suggest you may enjoy some history of the founding fathers’ concerns that the presidency never fall Into hands of anyone having loyalties to Great Britain especially or other foreign governments. Best regards,