The controlling law is the Immigration and Nationality Act, Pub. L. No. 82-414 § 301(a)(7), 66 Stat. 163, 236 (1952).
The foreign-born child is not a citizen if the citizen parent does not meet the requirements of this statute. The foreign-born child is not a
citizen by birth, the foreign-born child is a citizen by statute. A citizen by statute is a naturalized citizen.
http://uscode.house.gov/statviewer.htm?volume=66&page=163
>> A citizen by statute is a naturalized citizen <<
Well, I’d say that depends on what the meaning of “is” is.