If you were born outside the country, your father was not a citizen and you were illegitimate, then the rules were different. That's all people are saying, although the poster you responded to perhaps did shortcut the whole explanation.
Seems that it wasn't all that common for our honored ancestors of the era of our founders to have "real marriages".
It that you Dr. Bellesiles?
Jumping the Broom was pretty much the name of the game.
Jumping the Broom was an African slave thing.
In those days marriages were not recorded, nor even "sanctioned" by the state, but rather by the Church. So you have to check church records, or in some cases family bibles. Births too were not recorded by the state, but often were in the family Bible.
By the mid 1800s people in the US did indulge in more formal marriages and church people were generally more literate and knew how to keep a record.