An we know this for a fact...how?
The fact is that we are all guided by our opinions of what the framers meant...because they never bothered to define the exact meaning of those fateful words. The subsequent citizenship laws define the terms "citizen" and "naturalized citizen" -- but fail to address "natural born citizen".
So we are where we are, reliant on disparate opinions.
As I said, the word "Citizen" is defined by it's origin. It came from Switzerland, and the only reason it became in common usage in the USA was because Vattel's book brought it here.
The NORMAL English word at the time was "Subject." For a nation that initially intended to create a "King" of America, this is a perfectly reasonable word. This word "Citizen" was used in the Declaration of Independence, (1776) 12 years before they had decided that we wouldn't have a King. Don't you think that is a little premature for overturning the normal word usage to describe a member of a Kingdom?
No, the word "Citizen" itself identifies it's origin and purpose. It came from Vattel, and it was meant to signify a change in the nature of government from Monarchy to a Republic. (Like the Swiss had at the time.)
Vattel and the Swiss Republic used the word "Citizen" (Citoyen) and so we came to use the word for precisely the same reason. We too were a collection of independent states who were joining together to create a confederated federal Republic.
Monarchist words were no longer welcome to describe the members of this new society.