No man, I never meant your legal examples were not factual, they are just not pertaining to the Constitution’s NBC requirement, which has never yet been defined per the US Constitution. There are only two chances they will ever be defined, slim and none.
If today's legal system conceded original intent as binding in this clause, it would set a precedent that original intent is binding in other clauses. It would overthrow the legal theories that are the basis of every accredited law school.
It might be interesting to see if someone is clever enough to disqualify Cruz without resort to original intent.