Hey buddy- I was born to TWO American parents, but because I popped out on Canadian soil, I can always be Canadian (I'm currently not) but I can never be an American President. My father grew up to become a senior diplomat with the Department of State. His first job was qualifying applications for immigration, naturalization and citizenship status, so he knows ALL the rules.
He looked it up on my behalf and out of professional curiosity and nothing has changed in 220 years. If you weren't born on American soil, you can't be President. It's pretty simple. If I can't with two American parents, then Mr Cruz with only one certainly can't either.