Actually, it does. loana For President!
You are exactly right.
This is not about merely being a citizen. It is about being able to demonstrate that you are a “natural born citizen” such that you are *eligible to serve as President of the United States.*
It’s not clear yet (until the SCOTUS addresses this, if it ever does) if “natural born citizen” is determined by birthplace alone, descent alone, or a combination of birthplace and descent (and if descent, then from whom-—mother, father or both).