Washington, Adams, Jefferson et al were born in the colony of America under British rule and became citizens with the adoption of the Constitution. They feared for the future when, for example, a British subject born here in the US, might have dual loyalties, hence the strict language which makes it (natural born) -a unique requirement for the POTUS and Vice Potus.
Natural born, i.e., born in the USA to American citizens. McCain and Obama are both not natural born, unless the Supremes rule differently. Could go on but you'll find it all at www.naturalborncitizen.wordpress.com.
I've never seen any evidence in their words that they were concerned about that.
There is a great amount of evidence that they were concerned about immigrants gaining the office.
My mistake: the comments I was thinking of were actually about foreign influence in the election, especially the re-election, of the President.
The Jay letter is the only direct comment on this AFAIK.
A native born citizen is a natural born citizen though a natural born citizen may not be native born. Descent from citizens makes one natural born even if born in China. Mere geography makes one native born. One is either natural born or naturalized. McCain needed no naturalization since he was the child of US citizens making him natural born.
You point to the correct point but manage to miss it. Allegiance is the point of requiring natural born citizens be president. There is nothing which disrupts that allegiance in children of citizen agents of the government being born abroad. In fact, such an origin amplifies the allegiance required since the parents are serving at the behest of the nation. It is a total contradiction of the entire intention to declare children of ambassadors, FBI agents, even Congressmen, and military officers ineligible of a right the child of an illegal alien has.
Geography cannot stand against allegiance. None of the Founders were “native born” within the USA since it did not exist. And slaves and Indians would be native born after 1787 and therefore eligible. Hence the term Natural born.