I agree with you.
My parents, at the time of my birth, were BOTH British subjects. My mother worked for the British Army during
WW2. While they were here on Green Cards, their allegiance could still be said to lie with the UK.
Hence, while I was a “Citizen”, I was not a “Natural Born Citizen”.
I learned this over 30 years ago from someone I would regard as very knowlegeable on the subject.
I don’t think the law would be that inflexible if it came down to it, no matter what argument can be made. The public and the courts would find them unreasonable.
You can run for president without worries !