The term “natural born” applied to most of the founding fathers - they were “natural born” subjects of England - most of whom were NOT born in England. Obviously the term as they understood it did not include having to be born in the nation. According to English law birth place was not the primary consideration - as one Brit pointed out when people said he was Irish (he was born in Ireland) “being born in a barn doesn’t make one a horse.”.
The “higher standard” still applies just as when the Constitution was written - of the three types of citizen the Constitution establishes - naturalized citizens are excluded from the Presidency.
Is Sen Ted Cruz a naturalized citizen? No. He is not.
It does no such thing.
Actually, that's not true. Under common law the primary consideration was indeed place of birth.
BTW, the Irish guy you mention was the Duke of Wellington.