That is a definition, but it is probably not the correct definition. Until Barack Obama ran for President, every definition of US citizen I ever ran across only mentioned two catagories:
Natural born citizens, who got their citizenship at birth
Naturalized citizens who got it after they were born.
The both parents must be US citizens definition appears to come from a French legal text and is, to me, not relavent.
I’m a strict constructionist. The plain meaning of “natural born” means having that condition at birth. If someone is described as a natural born athlete, it means they were born that way. It does not mean that both of their parents were athletes and that they were born in a stadium.
It is only by examining the 18th century usage and definition of a term that we can ascertain its meaning in the Constitution. In the 18th century, and at the time of the framing and ratification of the Constitution by the states, the term natural-born subject or citizen was always used or defined in such a way as to exclude the child of a British or American girl or woman when that child was born in a foreign country and that childs father was a foreign citizen. No 18th century jurist would have thought the term natural-born citizen or subject could have been extended to the child of a British or American girl or woman when that child was born in a foreign country and that childs father was a foreign citizen.
Here is Blackstones classic exposition in 1765 of the legal meaning of the term from the Commentaries on the Laws of England.
William Blackstone, Commentaries 1:354, 35758, 36162
1765
Natural-born subjects are such as are born within the dominions of the crown of England, that is, within the ligeance, or as it is generally called, the allegiance of the king; and aliens, such as are born out of it.. . .
When I say, that an alien is one who is born out of the kings dominions, or allegiance, this also must be understood with some restrictions. The common law indeed stood absolutely so; with only a very few exceptions: so that a particular act of parliament became necessary after the restoration, for the naturalization of children of his majestys English subjects, born in foreign countries during the late troubles. And this maxim of the law proceeded upon a general principle, that every man owes natural allegiance where he is born, and cannot owe two such allegiances, or serve two masters, at once. Yet the children of the kings embassadors born abroad were always held to be natural subjects: for as the father, though in a foreign country, owes not even a local allegiance to the prince to whom he is sent; so, with regard to the son also, he was held (by a kind of postliminium) to be born under the king of Englands allegiance, represented by his father, the embassador. To encourage also foreign commerce, it was enacted by statute 25 Edw. III. st. 2. that all children born abroad, provided both their parents were at the time of the birth in allegiance to the king, might inherit as if born in England: and accordingly it hath been so adjudged in behalf of merchants. But by several more modern statutes these restrictions are still farther taken off: so that all children, born out of the kings ligeance, whose fathers were natural-born subjects, are now natural-born subjects themselves, to all intents and purposes, without any exception; unless their said fathers were attainted, or banished beyond sea, for high treason; or were then in the service of a prince at enmity with Great Britain. [The italics are Blackstone’s]