Yes it does.
Before they can become US citizens at age 18 they have to prove they have “lived”in the US for 4 years by using proof of passports and travel documents.
Then they should see an attorney. According to Title 8 > Chapter 12 > Subchapter III > Part I > § 1401 > Paragraph G the would seem to be natural born citizens. That paragraphs says that a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years is a natural born citizen.
Really? What I read is " The following shall be nationals and citizens of the United States at birth: " and besides that was not the law in 1961....but then you knew that...
According to the State Department:
"In any event, the fact that someone is a natural born citizen pursuant to a statute does not necessarily imply that he or she is such a citizen for Constitutional purposes."
http://www.state.gov/documents/organization/86757.pdf