So that is my explanation of how someone can be a Natural Born citizen if both parents are not citizens.
You are describing a citizen. A naturalized citizen.
a natural born citizen is different. The reason the founders included the language was to insure the person occupying the top seat would have no other allegiances.
If your parents were citizens of another nation when you were born, they you could have split loyalties.
There is a significant and deliberate reason for choosing the wording as they did.