You thought wrong. There's nothing in U.S. law that says that.
The Constitution doesn’t say simply “citizen”, it says “Natural Born Citizen”.
Now if you can come up with any documentation or references FROM THAT TIME PERIOD that says “Natural Born Citizen” means just any old Tom, Dick, or Harry, then you might be right.
But no such references exist. All the references at the time make it clear that “Natural Born Citizen” is one born on American soil, BOTH of who’s parents are American Citizens.