"I believe that a person who is a citizen at birth is a natural born citizen."Apparently you do not understand the difference between a citizen, a born citizen and a natural born Citizen. Do you even know why the various eligibility requirements for presidents were put in place?
What is the difference between a born citizen (citizen at birth) and a natural born Citizen as required of presidents by our founders? How does the adjective "natural" further restrict the meaning of the phrase and why did the founders add it?
Why then did the founders, who were superbly elegant and articulate, not simply write "born citizen?" Why would they insert the totally meaningless, superfluous (as you imply) adjective "natural" into a key phrase of the Constitution?
What further restrictive meaning does the adjective "natural" add to the phrase "born citizen" (i.e., citizen at birth)?
However, if someone creates a convincing argument that it can only mean one thing, then he or she should share that argument with the American people and if it is sufficiently convincing, the American people and their electors will accept it and employ it in selecting presidents. So far, I think most people seem comfortable with equating natural born citizen with citizenship at birth and I think that's what they've been doing.
See, one of the problems here is that most people see candidates like McCain and Cruz (both of whom spent their lives living in American neighborhoods, studying in American schools) as completely American. They don't see them as strangers to America who have come from some foreign land to subvert our system. So, using those people as examples of what the natural born citizen clause is designed to protect us from is counter-productive. When they see POW-United States Senator McCain, they don't see any great danger and they aren't motivated to narrow the natural born citizen clause in order to exclude his candidacy.
This year it looks like it's going to be Trump vs. Clinton. I guess there will be a few folks who will invent a claim that Trump is really the son of some Arab rug merchant or that Clinton was really born in France, but it won't work any better than it did the last time. Somebody will sell a few books and CD's, but most people won't be fooled. This kind of baloney - "The True History of So and So" - has become part of our electoral process. But, you're not required to take it seriously. You're not required to be a sucker. It doesn't mean anything in the long run.