While surfing around Wikipedia today, I came across an article describing honorary citizens of the United States. There was a note on Gilbert du Motier, better known as the Marquis de Lafayette. In it, the article noted (with sources, so I'm not just grasping at some Internet vandal's random screed):
"On 28 December 1784, the Maryland General Assembly passed a resolution stating that Lafayette and his male heirs ‘forever shall be...natural born Citizens’ of the state. This made him a natural-born citizen of the United States under the Articles of Confederation and as defined in Section 1 of Article Two of the United States Constitution."
Even though the Marquis was not born in Maryland, nor did he have any reason to be considered a citizen of the colony at the time he was born, by act of that state's legislature, they simply could define him as a "natural-born citizen." In other words, the status of natural-born citizenship is simply an issue of whoever Congress (who gained authority over immigration and citizenship issues when the Constitution was ratified) wants to define as natural-born citizens. They don't even have to be born citizens, technically speaking, as the Marquis's case demonstrates.
As Congress already bestows citizenship at birth to those born to American citizens, and has the authority to do so, there is no reason to assume this would not be natural-born citizenship.