The first statute passed by the first Congress says otherwise. But I do not wish to relitigate a matter which is now entirely moot. I understand this is a deeply held belief on your part and I am inclined to think that you are probably right but I am also bound to say that the question is not without counter arguments.
full I also happen to believe that in the view of the direction the litigation against Barack Obama took, which was never to reach the merits, the result would likely also obtain against challenges to Ted Cruz. This is a response on a practical level rather than on a theoretical constitutional level and I understand your position. The problem is getting your point of view litigated to a conclusion and a vindication.
Meanwhile I preserve a wee bit of humility on the subject.
That act was repealed and its replacement removed the mention of natural born citizen.
Even in the language of that repealed act, it stated that children born of citizens abroad “shall be considered as natural born citizens”, clearly indicating that they were not.