Please consider that the founding fathers drew upon their education, classical studies, common sense, and referenced many philosophical works. Vattel’s “The Law of Nations” [1758], a contemporary treatise on the natural rights and responsibilities of nations, would have been one such source.
http://www.constitution.org/vattel/vattel_01.htm
BOOK I.
OF NATIONS CONSIDERED IN THEMSELVES.
CHAP. XIX.
OF OUR NATIVE COUNTRY, AND SEVERAL THINGS THAT RELATE TO IT.
§ 212. Citizens and natives.
The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights. The society is supposed to desire this, in consequence of what it owes to its own preservation; and it is presumed, as matter of course, that each citizen, on entering into society, reserves to his children the right of becoming members of it. The country of the fathers is therefore that of the children; and these become true citizens merely by their tacit consent. We shall soon see whether, on their coming to the years of discretion, they may renounce their right, and what they owe to the society in which they were born. I say, that, in order to be of the country, it is necessary that a person be born of a father who is a citizen; for, if he is born there of a foreigner, it will be only the place of his birth, and not his country.
While it is certainly true that Vattel, Blackstone, and English Common law formed the basis of the Founders legal education it is also true that they changed the nature of the legal system into a uniquely American one.
Your quote indicates Vattel equated “native born and natural born” which is something I suspected from the lack of a definition of the former in Black’s.
The likely unmarried status of Urkle’s parents complicates this even further and, as another poster indicated, his bastardy means his mother’s status was the ruling one IF he was born in Hawaii.