I've always assumed it's the dead guy who wouldn't rat on the lady friend who's telling the story. Just because you're dead doesn't mean you can't write a song.

As for the lady, I suppose, if you think she's stayed schtum to protect her poor old husband from knowing he's been betrayed, rather than because it would be pretty awkward to have to come out as an adulteress, maybe it's possible to sympathise with her. But I've often thought the song should end with the ghost confronting her as a hypocrite, going round in her long black veil and lamenting the guy whose death she brought about by keeping quiet.