You’re proving me right. What you quoted is about natural born subjects, not natural born citizens. Note: We don’t have Kings in the United States (except for Rodney or Martin Luther). It’s time to quit spreading lies.
That is why they called it “precisely analogous”, only saving the change from subject to citizen. In a republic, a natural born subject is called a natural born citizen. So if you want to know the meaning the Founders assumed in the latter, see what was meant by the former.