“Rep. Bingham commenting on Section 1992 said it means “every human being born within the jurisdiction of the United States of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution itself, a natural born citizen.” (Cong. Globe, 39th, 1st Sess., 1291 (1866))”
“In the beginning of his definition, Vattel required that the children be born of “parents” who are citizens. The use of the word “parents” refers to both mother and father. If he required only one parent such as the father, he would have said “of fathers who are citizens” and not “of parents who are citizens.””
http://puzo1.blogspot.com/2009/09/natural-born-citizen-clause-requires.html
In Binghams's speech (not a legal citation) he was just restating the "under the jurisdiction" qualification that is written into the 14th. That qualification applies to the children of diplomats and invading soldiers, not to the children of non-citizens.
"In the beginning of his definition, Vattel required that the children be born of “parents” who are citizens...."
In fact, Vattel didn't define "natural born citizen" at all. He never used the term.
It also is more proper to say he was describing, not defining, the practices of most countries in Europe. He was a Swiss philosopher writing in French. A few passages down from what the birthers like to quote, he specifically notes that the rules in England are different and only birth on the soil is required.