I find it suspicious that that particular reference has been removed and a statement substituted which conveys a totally different meaning. Inquiring minds wonder why and why now.
Well, I have a guess, if you'd care to hear it.
My guess is that was something that had been sitting there for awhile, and something to which nobody was paying much attention. Eventually, someone drew attention to it. And once that happened, someone made the decision to scrub it.
Why? Well, because it had absolutely no business being there in the first place. It is not the role of the State Department to determine what constitutes a "natural born citizen" -- it just has nothing to do with them. That is the business of the federal courts, or Congress, or maybe even the state courts or state officials to determine eligibility to be placed on a ballot. But it looks to me like State had a summer law clerk with a little too much time on his/her hands, so someone assigned this as a dumb project.
In any case, the State Department's view of what constitutes a "natural born citizen" is entitled to zero legal deference. So it was "scrubbed" because somebody finally asked the question "what the hell is this doing here"?
Well I don’t agree.
This is a manual so that the State Department is consistent in its approach throughout the world and uses up to date policy information. Many freepers report being told by the consulate when they applied for citizenship for their offspring born abroad that they were not eligible to become President. My read is that they were told that because that was what was in the manual.
The Consulate does indeed need to know the statutes to be able to process the citizenship requests of citizens for their offspring born abroad. The original verbiage was there for many years and was based on the legal consensus. It was scrubbed because it was inconvenient for someone.