Well, in the case of Cruz, His parents were clearly American (Texas) citizens working Calgary oil fields in the service of US Commerce and the American dream. In the case of Barry Obama, his Piss Poor excuse of a Pappy was clearly a Kenyan working the US education system for himself. Obama Sr had no allegiance to the USA. That is the crux of Barry's ineligibility.
Obama has so many areas of doubt and potential conflict in this regard that it's difficult to know where to begin. The reality is so wacky it beggars belief, which has been used to advantage to discredit opposition and to confuse the public.
Obama, Sr. can plausibly be claimed to have been an official of a foreign government while here as a student. His own citizenship is a tangle due to the dissolution of the British Empire, but the upshot of it all means that the UK claimed sovereignty at birth upon the individual known today as Barack Hussein Obama, due to his being born to a subject, yes they were still subjects then.
Then we have his adoption, introducing another foreign claim of sovereignty. Then, the passport kerfluffle. There's so much spin and obfuscation there, so much misdirection over that one. I think he just got an Indonesian passport and traveled under it, which became a problem once it was determined he was running for President, then came the wild disinfo campaign.
Then, the foreign student thing, smoke there too, all records sealed.
Obama was not natural born eight ways from Sunday, imho, regardless of where he came into this world.