“The definition of natural born citizen requires that both parents be citizens of the US.”
YOUR definition. It just doesn’t happen to be the same as the one the states, Congress & the courts use...
“As the President is required to be a native citizen of the United States…. Natives are all persons born within the jurisdiction and allegiance of the United States.”
James Kent, COMMENTARIES ON AMERICAN LAW (1826)
“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,…A very respectable political writer makes the following pertinent remarks upon this subject. “Prior to the adoption of the constitution, the people inhabiting the different states might be divided into two classes: natural born citizens, or those born within the state, and aliens, or such as were born out of it.”
St. George Tucker, BLACKSTONE’S COMMENTARIES (1803)
Operative words: "and allegiance".
If a person received citizenship in another country at birth from his father, the argument is that his "allegiance," as that term of law was understood at the time, was to that foreign country. This is exactly what the Founding Fathers wanted to avoid -- e.g., a French prince fathering a son with an American, making the son a French citizen as well, and the son later taking power over the United States as President, while a French citizen by birth.
Your first example refers to native born citizen...your second also and ignores the issue of parentage. It’s too bad the term is not defined more clearly, but I suppose the letters of the drafters would shed some light. If I was more motivated, I would research them, but alas, I am not. Unless someone cam convince me otherwise, I would say that Obama Sr’s alleged British citizenship would disqualify the junior.