John Reavey in his introduction to the ballad used to say that Hughie was hanged because he got the beter end of the deal

I like (and use) the version that suggests the horse was just a pretext -

"And give this word to Maggie my wife
The next time you go o'er the moor
Tell her she stole the bishop's mare,
Tell her she was the bishop's whore."

Hughie Graham was framed!