According to John meredith & Hugh Anderson book "Folk songs of Australia and the Men and Women Who Sang Them" that Arther Buchanan and a Fred Sloane learn Waltzing Matilida well before Paterson was meant to have written it according to the Paterson-Macpherson legend.What most people fail to remember that Paterson was a collector of "Old bush Songs" during that period and eventually published in 1905 a book titled "Old Bush Songs Composed and Sung in the Bushranging, Digging and Overlanding Days".
It is quite possible that Paterson heard the song, cleaned up and/or added to the words and was looking for a tune to go with it. what supprise me as someone who has read a lot of Paterson verse is that Waltzing Matilda isn't in a similar style.
Bruce