Seriously? You've already forgotten what your expert wrote: "Prior to this time the subject of citizenship by birth was generally held to be regulated by the common law, by which all persons born within the limits and allegiance of the United States were deemed to be natural-born citizens thereof"? I just posted that this morning, and now you're claiming that what "allegiance" means has nothing to do with Natural Born Citizen?
That excerpt applies to anyone.
First of all, if it doesn't imply they're a natural born citizen for Constitutional purposes, it certainly doesn't imply they're not. Second, it applies to someone who's a "natural born citizen pursuant to a statute." People who are natural born citizens because they're born here are not NBCs pursuant to a statute. The 1866 civil rights act and the 14th Amendment didn't make up anything new, they were just "declaratory of the common law" (in the words of your expert). And remember what the common law said? (Hint: it's in my last paragraph.)