Here's the problem we face when discussing the meaning of natural born citizen(NBC) in this particular context. Many people, apparently, wish to evaluate a US citizen's eligibility to be viewed as an NBC, by some application of foreign statutory law. Why would we do that, ever?
To take the argument to the absurd extreme, what would keep one of our enemies, like Korea or Iran or even Russia, from extending - by statute - citizenship to anyone with Iranian/North Korean/Russian blood, irrespective of how many generations that person could actually be removed from those countries. Using the same logic that many apparently wish to apply to Kenya or British or Indonesian law, anyone who was of even negligible of Iranian or North Korean ancestry, would be foreclosed as an NBC precisely because they would now - by statute - be North Korean or Iranian ancestry. Now, does that make logical sense?
The King had no need to declare young Barack Jr. a citizen of the British Empire. He was one at birth.