Just as it is dangerous to presume that the "first publication" date is necessarily tied to creation of a work, it is (I think) similarly dangerous to presume that "broadsides" were ever the sole means of transmission of a song.
--paddymac
This is an interesting point. And it leads me to ask this question: is it ever possible to prove whether or not any song or piece of music has been transmitted solely by either aural or written means. I would submit that it is not.