Bronson's analysis (part of his essay All This for a Song? 1962) is, as Toadfrog says, sensible and well-informed; unlike Robert Graves' fanciful imaginings which, like most of his comments on traditional song, appear to owe as much to herbal tea as they do to scholarship.

I don't know if Mrs. Knipp the actress, from whom Pepys heard the song, was herself Scottish; he said "...in perfect pleasure I was to hear her sing, and especially her little Scotch song of Barbary Allen."  This (1666) is the earliest known reference to the song; as Bronson points out, it is unlikely to be older than the mid 17th century, and likely gained greater currency through stage performance, and through the printing of a Scottish text in Ramsay's Tea-Table Miscellany of 1723/4, and of that text and another from an (earlier) English broadside of Pepys' time in Thomas Percy's immensely popular Reliques of Ancient English Poetry ( 1765).  It continued to circulate on broadsides, in reasonably consistent forms, until the final years of the 19th century.

As Toadfrog says, the earliest known version of the song does not speculate on motivation, though later versions introduce it.  Traditional song tends not to examine underlying motive, being concerned primarily with pure narrative, and it's usually a mistake to try to impose modern sensibilities upon such things; they should really be accepted for what they appear to be at face value.  Of course, the obsession with unearthing "deeper" meanings is not new, but it has always led to more misunderstandings than revelations.

Bruce Olson has the early text at his website, as he mentioned long ago when this thread was young:  Barbara Allen's cruelty,  and a later, very close, broadside text can be seen at  :

Barbara Allen's cruelty: or the Young man's tragedy  Printed in Newcastle; date and printer unknown.

There are of course many other broadside examples at the Bodleian site, mostly 19th century.