Part II -- What constitutes a status of "natural-born citizen"?
The text from Part I is from the Naturalization Act, codified in the United States Code, and in effect as of this writing.
Now here is where the controversy starts to get very muddled, people seem to have glommed onto the text of the 1940 Naturalization Act, Chapter II--Nationality At Birth, which read differently:
(g) A person born outside the United States and its outlying possessions of parents one of whom is a citizen of the United States who, prior to the birth of such person, has had ten years' residence in the United States or one of its outlying possessions, at least five of which were after attaining the age of sixteen years, the other being an alien: Provided, That, in order to retain such citizenship, the child must reside in the United States or its outlying possessions for a period or periods totaling five years between the ages of thirteen and twenty-one years: Provided further, That, if the child has not taken up residence in the United States or its outlying possessions by the time he reaches the age of sixteen years, or if he resides abroad for such a time that it becomes impossible for him to complete the five years' residence in the United States or its outlying possessions before reaching the age of twenty-one years, his American citizenship shall thereupon cease.
The final blow to the Birth Certificate controversy is covered in Part III.