Yes, I do believe that is accurate, and as one can plainly see, Congress has made what it thought to be necessary changes at times to increase the level of security that the law provides to the country. They have also decreased it as the risks mitigated over time.
In effect I believe that the law can be tweaked when required by adding or subtracting requirements that define natural born..But to change the substance of the law would require a constitutional amendment. In my layman opinion.
I was taught in high school that the reason that the founders specified that the president be a “natural born citizen” was to avoid having someone with divided loyalties ascending to the presidency. How this plays out legally in Ted Cruz’s case has not to my knowledge been decided by the courts. I am not a lawyer and not sure that other cases cited actually apply to this specific set of circumstances. I believe that Cruz himself should ask for clarification. With his sincere cooperation I would think that a binding decision could be made quickly. I don’t think that the tactics employed by Obama and his surrogates will work in this situation.