All very interesting. Like a lot of stories about folksongs (if soemthing as well documentedas this could be called a folksong)thevarious accounts leave unanswerable questions. Christine McPherson's tune is reputedto have been said by her to be what she remembered of the Craigielea tune, as arranged by a man called Bulch, played at a concert some time previously. We dont know how good her memory was, but the fact is that her tune isnt the Craigielea tune. Another fact is she hadnt mastered musical notation, and her manuscript doesnt make sense(in the chorus anyway).Howeer, you can see roughly what shemeant, and it is undoubtedly the basis of the modern tune. I would guess that, whether or not she could or couldnt remember anything of Craigielea, she certainly had a bit of Mozart in her head for the chorus. Or possibly the bloke who reworked her tune was remembering the Mozart, as his version of the tune is closer to Mozart than hers was. A lot of ifs and buts!
However, going back to the original topic, what is undoubtedly 100% certain true is that Robert Tannahill had no hand in Waltzing Matilda, words or music. Well, probably.