I am not an expert on any of this but I see problems with this interpretation. A mother who is a US citizen could be living in say Australia and has a child with an Australian. The child is a US citizen andd finally comes over to the US when he is 18. I would not view that child as a natural born citizen. I think youi have to be born in US and become a ctizen at birth. That’s just what makes sense to me and defer to others.
Under your scenario, illegal aliens would eligible (which they are not) and the babies of US servicemen who wives give birth in foreign country would ineligible (which they are).
The Cruzes were Canada for work, not to seek Canadian citizenship.
It would seem that the reasoning which would make Cruz eligible could also apply to Obama, even if the latter were born in Kenya, after all.
Cruz — born in Canada, but mother was US Citizen, so that makes him eligible?
Obama — born in [Hawaii/Kenya], but mother was US Citizen, so that makes him eligible?