Yes, that is the case.
Which isn't surprising. If you're parents never brought up your dual citizenship when you were a kid, it isn't likely that you'd have given the issue much thought.
Sure, you were born in Calgary, Alberta but, so what? You were an American citizen, just like the kids born to military families overseas.
“Just like the kids born to military families overseas” is he object of debate. Military and Foreign Service fall into their own category. I have been told by military families who have a kid or kids born overseas that they had to go thru some paperwork to get those kids’ citizenship status worked out. Even more so would be the case for someone engaged in private enterprise.
I have no idea what Cruz knew or when he knew it, but he’s an extraordinarily bright person who managed to get thru Princeton and Harvard Law School. One would think that somewhere along the line he’d have questioned his citizenship status, knowing at a minimum that he was born outside the United States.
Seriously, he’s known for years now that ultimately he wanted to run for POTUS. He can’t have missed the brouhaha over Obama. And he never wondered what his own status was? Dunno, but that lack of curiosity sure strikes me as interesting.