Actually, the NBC issue does relate to the VP, as the VP could assume the position of POTUS. The NBC issue relates to any person who could be inline to assume the office of POTUS.
True, he can’t be POTUS, but that just means it slides down the line of succession. There is no NBC requirement for the various offices and posts that are in that succession.
The philosophy of this nation is such that the last live American would be sworn in if there was a judge to do so. Command always devolves to the next in line and every single one of us is in that line. Native born following natural born and naturalized following them.
And no! that is not codified in the law.