originated in a Broadsheet.
Is there any evidence that the broadside hack didn't get the song from the oral tradition?

One reference point is whether the existence of the song was ever noted before it was published.

This does sometimes happen, as with "The Braes of Balquhidder" or the song that was the model for "Johnny Cope", but it isn't anywhere near as common as the situation where nobody at all had ever heard of it before Stationer's Hall did.

And I don't see why you want to insult someone like John Hamilton (who wrote the first known version of "The Braes of Balquhidder") by calling him a "hack".