A clue to the problem with  Arbutus  lies in the attribution: "trad/grater".  Apparantly, this should be [Paddy] Graber, who has taken some bits of Willie O' Winsbury and drastically rewritten the song.  The transformation into a tree business doesn't appear in any of Child's examples, or in any other version that I've ever come across; that, presumably, is entirely Graber's invention.  That being the case, it's also quite likely that he set it to another tune; all the traditional examples I know of (including the one Sorcha quotes) are sung to variants of the same melody, with the fourth line of each verse repeated as a refrain, which would be one reason why the Child melody doesn't fit "Arbutus".  There is an example, collected by Cecil Sharp in the early years of the 20th century, at  Willie O' Winsbury,  though the accompanying text is from elsewhere. Actually, the tune best-known nowadays for Willie was composed for that very set of words by (I think) Andy Irvine in the 1960s; it was almost instantly assumed to be traditional because it was so convincing, and Fairport Convention set  Farewell, Farewell  to it on that assumption.  That tune fits "Arbutus"...

Malcolm

P.S.  Sorcha: which of Child's examples does the tune you posted belong to?

PPS.  MMario: that means that "Farewell Farewell" needs to go back on the "Missing" list, as the "Willie" tune in the DT is the wrong one for it.