No, it's because one of his parents wasn't a US Citizen.
British law isn't the issue.
I completely agree that both parents are required to be citizens for one to be NBC (including being born "on soil").
However, any idea WHY that needs to be so?
It's so that the parents can NOT "convey" their foreign citizenship onto their children. The parents aren't the one's trying to run, or that obtain, the office of the Presidency. It's the children who grow up to. Those same children that would be born with divided loyalties is what the framers wanted to protect against. And that's exactly what happened here.
So the question isn't, how can Barry's father who was never a citizen have a son who can never be NBC because he (Sr.) was a foreigner?
The question is:
HOW CAN A NATURAL BORN CITIZEN'S STATUS BE "GOVERNED" BY GREAT BRITAIN?
The former argument can lead to years of debate. The later question has yet to be "justified" or answered in any way shape or form by anyone so far as I know.