You can also see my post #57 where I went into even greater detail. 🙂👍
Bottom line here is, 4 of the Presidents were involved in the crafting of the Constitution, and they certainly would not have eliminated themselves from being President or Vice President of the nation they had played a continued role in their creation in its infant years.
Busy afternoon - until I get to the links let me say re your "bottom line" - they provided very well for their Constitutional qualifications; it was enough that they were citizens, NBC simply didn't apply to them.