A "natural born citizen" is someone who was a citizen at birth. The child of a U.S. citizen parent qualifies by definition.
Everything else is chasing figments of the imagination. Going back to the drafting of the constitution, the whole point of the citizenship requirement was to ensure that no political faction would be tempted to import a European figure with a title and possible star appeal, naturalize him after 90 days in Massachusetts or South Carolina, and reinsert the aristocratic principle into American politics. It really is that simple.
Bringing in a foreign born king to satisfy a political and religious requirement, King William of Orange because he was Protestant and married to the daughter of Charles II, and the German Hanoverian dynasty (George III anyone?) were recent history for the founders. And some people were all for establishing an American constitutional hereditary monarchy as the most successful model of government existing at that time. Later in the 19th century Mexico had to overthrow just such a transplanted monarch, Maximillian of Austria. So it was not a ridiculous notion.