There are two problems with all the attempts to link "The Bold Fusilier" with "Waltzing Matilda." First, despite what everyone claims, there is no firm evidence of the existence of "Fusilier" before 1941, and the fragment we have (it's only a fragment) doesn't really sound like it comes from the reign of Queen Anne.

Second, although the version everyone sings of "Waltzing Matilda" appears to be that of "Fusilier," the common version was reinterpreted by Marie Cowan, and is not the same as the tune supplied by Christina MacPherson. MacPherson's tune is supposed to be "The Bonnie Woods of Cragilie," misremembered. I can't really speak to that. I do sort of wonder if Cowan had the "Fusilier" tune in her head, and corrected MacPherson's tune to get it right, but I can't prove it. We have no evidence.

I will not say that the "Fusilier" is a red herring in the history of "Waltzing Matilda" -- I genuinely think Cowan may have known it -- but I don't think either Banjo Paterson or Christina MacPherson did.

I spent months studying this. Most of my conclusions (8000 words of them) are in the Ballad Index entry on "Waltzing Matilda", http://balladindex.org/Ballads/PBB119.html, but there is also a bit in the notes on "The Bold Fusilier": http://balladindex.org/Ballads/DTcombso.html.