The Founders used the terms natural born and native born interchangeably. The best example is St. George Tucker’s statement.
“That provision in the constitution which requires that the president shall be a native-born citizen (unless he were a citizen of the United States when the constitution was adopted,) is a happy means of security against foreign influence, which, where-ever it is capable of being exerted, is to be dreaded more than the plague.”
http://press-pubs.uchicago.edu/founders/documents/a2_1_1s18.html
There is also the statement by Congressman Hillhouse of Connecticut during the 1795 debate over the Naturalization Act, that the children of an alien father would be natural born citizens.
‘a happy means of security against foreign influence, which, where-ever it is capable of being exerted, is to be dreaded more than the plague.”’
Obama certainly proved this point. He never made a decision that favored the US over foreign interests.