It has everything to do with it. It is the law of the land now and was then. Cruz was born of one US citizen parent in Canada, which also confers birthright citizenship automatically on Cruz. In essence, Cruz had dual nationality at the time. He only recently, in writing, renounced any claim to Canadian citizenship claiming he did not know he could opt for Canadian citizenship. He could have applied for a Canadian passport in much the same way that Obama could have applied for a Kenyan/British passport since his father was a citizen of Kenya.
The issue I raise is that if you use the criterion that a NBC under the Constitution means any US citizen who does not require naturalization to become a citizen, then this opens the door for the US born children of illegal aliens, green card holders, and tourists. All such children are US citizens at birth.
Yes, they are eligible. Which just means they aren't legally disqualified from office. They'd still have to win the election. There doesn't have to be legal disqualification against everyone we don't want to win.