“Sounds to me like whoever told you that was full of crap.”
I was born five days before D-Day and was taught all through school until I joined the Navy in 1962 that natural born citizen meant you had to be born on American soil and have two citizen parents. That is what people grew up believing because that is what they were taught in school. I never heard anything different. My wife is eight years younger than I but she was taught the same thing in school. Make what you will of it but it was taught as gospel for many years.
Personally, I think it should take both parents having many years of residency in the US under their belts as well as the child born, a requirement on having grown up in the US, but that's me. Pretty obviously, the spirit of the thing is to prevent a foreigner from becoming president. Cruz is as American as apple pie. It's as simple as that.