But we don't have to guess about this. The Constitution was written in Philadelphia in 1787, and the legal community of Philadelphia knows best what it meant by the reference to "natural citizen."
In one of the most prominent law books in Pennsylvania, and one which was based on the work by their Supreme Court, they explicitly say the American understanding is based on Vattel, and not on English Common law.
What subsequently confused the nation was the efforts of people like Rawle to assert our citizenship was based on English common law in his misguided efforts to apply this legal doctrine to the issue of slavery.
He deliberately pushed the English law claim while knowing full well it had been rejected by all of his peers in the legal community of Philadelphia. It was in fact, rejected by the Pennsylvania supreme court in a case he brought for the purpose of freeing a slave, and in which he collaborated with William Lewis, the man Solely responsible for the legal education of Samuel Roberts, the man who compiled the above mentioned book.
Rawle was a deliberate liar on this point. He wasn't mistaken. He had been fully informed of the truth, and deliberately misled people about it.