I don't think Graber based it on any specific story, though people used to turn into trees all the time in the old days; a nasty habit which is rather discouraged nowadays.  I suspect that he was thinking of A.P. Graves'  My Love's an Arbutus,  though I could easily be wrong.  The Willie of Winsbury story is just a starting point, and scarcely a word of any traditional text is retained in his song so far as I can tell.

We're still looking for the tune for the DT, incidentally; can anybody tell us what it was?  I referred some time ago to the best-known (nowadays) Willie of Winsbury tune as a possible composition of Andy Irvine's, but I had only partly remembered the story; in fact, he set a text he found in a book (unspecified) to a tune from an unspecified "book of ballads" for a record he made with Anne Briggs, and only realised when it was too late that he'd been looking at the wrong page.  I did a bit of research a while ago, and discovered that the book was (hardly surprisingly) Child's English and Scottish Popular Ballads, and the tune really belonged to Fause Foodrage; the tune for Willie was on the next page but one.

Nobody seems to have realised that at the time (and I've never seen anybody make the point since, for that matter) so it's perfectly possible that Graber may have used that tune under the impression that it was appropriate; alternatively, he may have made up a completely different one of his own.  Somebody please tell us!