I'm watching the game too, sort of.
The Indians were NOT made citizens of the US. They were citizens of their own nations. This was a deliberate exclusion.
-- This left congress to determine who a citizen is. As it should be. --
As it is. Congress absolutely has that power. What the constitution aims to cut off is congressional power to expand the pool of presidents via acts of naturalization. There are two ways an "invader" could obtain qualification. One would be your Mexican invader example, born on US soil; the other being a Congress that was liberal with regard to naturalization of birth abroad.
The principles at work are highly nationalistic. As national barriers are broken down, and nations merge into "one world," all that nationalistic stuff can go in the crapper.
I read all that some time ago, and my memory may be a bit vague however I recall that Indian nation citizenship was indeed carved out and allowed but they were encouraging them to pledge their allegiances to the United states and the natural born citizen was the legal out for them to accomplish this. In other words they left the door open for them and any others who were born on the continent or territory and wanted citizenship and legalization.
This is the difference between Hamilton's original draft and the eventual language. I will have to did into the federalist papers to see if I can find any discussion on it, but I don't think there is much..
John Jay in a letter to Washington said this...
"Permit me to hint, whether it would not be wise and seasonable to provide a strong check to the admission of Foreigners into the administration of our national Government, and to declare expressly that the Command in chief of the American army shall not be given to, nor devolve on, any but a natural born Citizen.[20]"
While the Committee on Detail originally proposed that the President must be merely a citizen as well as a resident for 21 years, the Committee of Eleven changed "citizen" to "natural born citizen" without recorded explanation after receiving Jay's letter. The Convention accepted the change without further recorded debate.[21](from Wikipedia)