In recent threads, a couple of minstrel songs have come up, from the ca.1850 era. Forgotten the details now, but one was issued in the U. S. in say, 1852. It was also issued in England the same year, but with part of an English-Irish song appended to make it more understandable to an English audience.
If we didn't have the actual data on its origin and dating, you can imagine what speculations would develop over its original provenance.

This just emphasizes your comments on songs like "Cockles and Mussels." The parlor songs of Edinburgh in the 19th c. often took up Jacobite or earlier themes. Song writers who know a bit of history can give their song the feel of something quite old. One hundred or more years later, if the original has been lost, we would have posts arguing its age.