Those academics who have done the groundwork tell us that any song referred to as 'Scotch' by the London theatre goers in the 17thc meant anything that was sung in any dialect from further north than Watford, and that included anything written in London that used such a dialect.

I would guess this description applied to the 'Sir John Graeme' variant in vague theatrical Scots, although the Reading/Scarlet version has earlier provenance in print. I would say to me it's pretty obvious that one is a pastiche of the other but I wouldn't like to guess which came first. In the 18thc there was a lot of Scottifying of earlier London pieces, just as at other times there was a lot of anglicising of Scots material.

Whatever, 'Barbara Allen' has been in constant popular print for nearly 4 centuries. This just adds a perspective to the fact that it is the most collected ballad from oral tradition.