7 FAM 1131.6-3 Not Citizens by “Naturalization” (TL:CON-68; 04-01-1998) Section 201(g) NA and section 301(g) INA (formerly section 301(a)(7) INA) both specify that naturalization is "the conferring of nationality of a state upon a person after birth." Clearly, then, Americans who acquired their citizenship by birth abroad to U.S. citizens are not considered naturalized citizens under either act.
7 FAM 1131.2 Prerequisites for Transmitting U.S. Citizenship (TL:CON-68; 04-01-1998) Since 1790, there have been two prerequisites for transmitting U.S. citizenship to children born abroad: (1) At least one natural parent must have been a U.S. citizen when the child was born. The only exception is for a posthumous child. (2) The U.S. citizen parent(s) must have resided or been physically present in the United States for the time required by the law in effect when the child was born.
http://www.state.gov/documents/organization/86757.pdf
That isn’t all the Dept of State says:
“However, dual nationals owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries. Either country has the right to enforce its laws, particularly if the person later travels there.”
http://travel.state.gov/travel/cis_pa_tw/cis/cis_1753.html
On the first point, they do. But not on the second, they agree that there are residency requirements for the US citizen parent(s).
I wish they would refer to section of the US code rather than the Act that generated it. Makes looking it up easier....ah, here it is. 8 USC 1101 (definitions). Yes it says what the manual indicates.
I think it's a matter of interpretation. And in general doesn't matter anyway, since naturalized citizens and other citizens have exactly the same rights. The other seciton of the law refers to "citizens at birth" it is true, but the law was passed under Congress power to define a uniform rule of naturalization. So how can persons whose citizenship depends solely on such a law be anything but naturalized? The part you quote from the state department is not the law, just their interpretation of it.
The State Department, in the same Manual says (in the section immediately preceeding the one you quoted:
The law which replaced the 1790 act, in 1795, said the same thing, without the two words "natural born". And so the law remains today, that a child of US citizen parents, born outside the US, is still a US citizen.