Nope, that's not what it says. When it relates the particular facts about McCain, it is *not* creating a "definition" of natural born citizen.
In effect, it says, "these are the facts about McCain and so he's a natural born citizen". It does NOT say, "only these facts would qualify one to be a natural born citizen".
You are misreading it into what you want to believe it says.
Sorry — read it again. The definition of “natural born citizen” is embedded in the text. It is “understood” by those who wrote it and those who read it.