Cruz is eligible as per the 1952 statute defining the NBC.
First the applicable statute:
http://uscode.house.gov/view.xhtml?path=/prelim@title8/chapter12/subchapter3&edition=prelim
Other documents relating to this matter:
http://www.cato.org/publications/commentary/yes-ted-cruz-can-be-president
http://eaglerising.com/20923/is-ted-cruz-is-a-natural-born-citizen-the-short-answer-is-yes/
All these sponsors of the debates have agendas.
Since National Review has comes out against Trump, that should be disqualified from sponsoring the debate.
The rule you advocate allows a US citizen mother to marry Achmed the mad bomber, and their child, born and raised in Iraq would be NBC of the US for his whole life, even if he never set foot in the US. I'm not saying eligible for president, that takes 14 years of residence.
The entire, and I mean ENTIRE weight of precedent on the subjects finds that foreign-born citizens are naturalized citizens.
I've studied this. I've written thousands of words citing the law and precedents, go through my FR history, I'm not going to discuss the issue with you. You believe whatever you want, I'm good with that.