Well, the wellknown tune is a different matter, much discussed.
Some aver it to have been English, on hotly rejected grounds.
Burns offered the tune he heard - 'from an old man' if memory serves -to his publisher, who preferred another tune - had Burns not already used the 'original' tune for something else? Jim, how much of the text do you think is 'trad' and how much written by Burns? He mostly seems to have kept just the first verse and chorus, and made / remade the rest, but I've not seen a discussion on this.