That’s a good catch. However, there is a difference between a natural-born citizen and one who is naturalized.
What does the “natural-born citizen” law of that time read?
1790 First Congress, Act of March 26th, 1790, 1 Stat. 103.
"And the children of citizens of the United States that may be born beyond the sea, or out of the limits of the United States, shall be considered as natural born citizens: Provided, That the right of citizenship shall not descend to persons whose fathers have never been resident in the United States".
It has been modified or superseded over time to allow for citizenship to pass through the mother and to change the residency requirements to specific intervals, the 1934 Act previously cited being the first one to do that. Subsequently the residency requirements for a parent of a citizen and a non citizen to pretty short periods, and at the time of Obama's birth it was 10 years a resident, at least 5 after the age of 14 (1952 The Immigration and Nationality Act 301(a)(7)). Since Obama's Mama was too young at the time to meet these requirements, if Obama was born outside of the US or its possessions (say, in Kenya) he would not be a natural born citizen.
In the Act of November 14, 1986 301(g) (re-designated from 301(a)(7) in 1978) was modified to change 10 and 5 to 5 and 2, but that was after Obama's birth and does not appear to be retroactive.
Subsequently in The Immigration and Nationality Technical Corrections Act of 1994 the residency requirements were extended to include grandparents (if granny met the requirements but mom and dad did not, you could still claim citizenship at birth).
What does the “natural-born citizen” law of that time read?
Thats the $64K question ...
From my research, I am of the feeling that, under the concept of “original intnet”, the terms “natural born citizen”, “citizen at birth”, and “citizen by birth” meant the SAME thing to the Founding Fathers.
As opposed to “naturalized citizen”.
Now, the FFs borrowed LIBERALLY from the Magna Carta and English Common Law, they also looked to Blackstone’s Commentaries on English Common Law.
Blackstone cites English precedent that children born abroad to two British subjects who owe their alleigiance to the King, and whose father is in service to the King, are INDEED natural born British subjects.
Since MOST of the lawyers in America at the time of the Constitutional Convention were trained in British Law, I believe that this would have been their interpretation.