Joe Offer wrote: "Dick Holdstock calls it 'The Bold Fusilier.'"

That's pretty much the standard title, and the one used in the Ballad Index. It's an assigned title, though, because the field collections are so fragmentary.

John Meredith talked to people who thought they had heard it before the Marie Cowan publication of "Waltzing Matilda," but that was so much later that the informants' memories are hardly to be trusted. It is important to note that the earliest records of the song seem to be from 1941 -- the very time when Australian soldiers were spreading "Waltzing Matilda" around the world, and it was being heavily parodied.

The flip side is, why would anyone make up a song about the War of the Spanish Succession in the twentieth century?

I repeat, this has been heavily, heavily debated. Australians tend to be fanatics about this. But the evidence is quite strong:

Christina MacPherson certainly did not know the Fusilier text (though it's barely possible that she had heard the tune and forgotten it).

Banjo Paterson almost certainly did not know the Fusilier text, at least consciously (although it's barely possible that some memory might have caused him to use the same verse form).

Marie Cowan may have known "Fusilier," or at least the tune, and adapted MacPherson's tune toward it. This is the one reasonable assumption in the sequence, but even it can't be proved.

It's worth noting that most of the people who assume "Fusilier" is the ancestor of "Waltzing Matilda" ignore the fact that the common tune is Marie Cowan's (significant) modification of Christina MacPherson's tune, not MacPherson's remembered version of "The Bonnie Woods of Craigilie."

It might also be worth pointing out that, while chorded zithers existed in MacPherson's time and she did play one, they were much less capable instruments then (fewer chord bars) and the techniques of autoharp playing used by, say, the Carter Family and brought to a high pitch by Bryan Bowers, had not been developed at the time. MacPherson's autoharp playing would have been much more limited than what one could do today. It probably could not play the ninth chord that many people use on "Waltzing Matilda" today, e.g., and it was not a melody instrument.

When I started researching "Waltzing Matilda," I felt quite sure that it was a parody of "Fusilier." After doing all the work, I am now convinced that at most, "Fusilier" influenced the Marie Cowan tune, and I'm not sure of that.