Hi Valmai,
The tune in the Digitrad is the first of two given in Bronson's Traditional Tunes of the Child Ballads (what, you mean you haven't ordered your four bargain volumes from Camsco yet?), which is from the celebrated Anna Brown of Falkland, Aberdeenshire - F J Child's favourite ballad source. It's a bit weird, but bear in mind that Mrs. Brown's tunes were transcribed by a nephew who wasn't necessarily very adept at the task.

The tune that Pete sings sounds very like one of his own - and none the worse for that.