I keep coming back to:
Ted Cruz is a citizen because he was born to a US Citizen (who did live in the US after age 14 for more than the required number of years). Nothing special had to be done to grant him citizenship. Therefore he is a natural born citizen.
Now I'm not a lawyer, and I didn't discuss this with the founders, and it may come to a Supreme Court case. But that's what makes sense to me.
(And ps - Obama born with "foreign allegiances"? What, to Kansas? Sorry, Excon, that doesn't fly)