There are two kinds of citizens: Born citizens, and Naturalized citizen. Cruz is not a NATURALIZED citizen because he did not immigrate into the country and become naturalized. He was already a citizen by virtue of his birth to an American Citizen mother. The location of his birth did not matter due to the fact that his mother was already a US citizen and had lived in the US for a number of years before he was born. There is actually a statute that defines all this. According to the statute, he IS a citizen by virtue of his birth, therefore a "natural born citizen".
Not so. There has never been an Article 5 amendment to the constitution about what is a natural born citizen. Therefore, the law stands as written IMHO. All originalists believe it takes both parents and born on the soil to be a natural born citizen. That was the definition when the constitution was written.