I think it's widely accepted that the tune at least is MacPherson's - even on his Celtic Viol album no lesser personage than Jordi Savall acknowledges that much! Not sure about Burns having much of a hand in it as a writer - certainly (most of) the five verse attributed to him don't feel like Burns, lacking his heavy handed mawkishness which ruins (for example) both Highland Widow's Lament and John Barleycorn, though I'll accept wretch's destinie! as being pure Burns in this respect, likewise the second stanza. The provenance of the other verses lies in The Tradition of the thing, although the great Davie Stewart felt certain of them were undoubtedly the work of MacPherson. In many ways, Stewart's version remains definitive, and the most authentic in terms of traditional provenance, with Stewart claiming descendancy from MacPherson, whose broken fiddle is extant, likewise the verses claimed to have been written by him, both of which you can see here:

http://www.clan-macpherson.org/museum/fiddle.php