Interesting. I count at least 3 possible origins of the story and we seem not to have considered the option that 2 or 3 of these may have contributed to the resulting ballad from oral tradition. The ballad writers, editors and oral tradition frequently mixed up facts from several sources over the centuries. Here's another example, the Child Ballad 'Geordie' actually has elements of 2 separate broadside ballads of the 17th century based loosely on real people, George of Oxford and George Stoole. The deliberate remaking of ballads by broadside writers and the likes of Scott has contributed in no small way to hybrid plots and ballads and material taken from one ballad into another.