The courts interpret the law - they don’t declare the truth. They use both common-law precedent and statute to determine what is meant by a natural-born citizen. Their decisions determine what the law is.
If the court rules that you’re a horse, then, for legal purposes, you are a horse.
I am very aware of this. The Courts are idiots, and like you said, they don't care what the truth is. The only thing they care about is that people do as they say.
You may be a horse per the common law you describe, which is a part of “Positive Law”, but you are not a horse per “Natural Law”. And the term “natural born Citizen” is a Natural Law term. That is what the adjective “natural” means. By Natural Law, not Positive man-made laws, amendments, or treaties. Most people don’t know the difference between Positive Law and Natural Law. First year law students are taught the difference but as soon as they get involved politically they tend to immediately forget it, for political agenda reasons of their client or political party or personal aspirations.