My opinion: if you're not adapting a trad song, it's just a cover. The question should be, are you doing it tastefully? Are you making it you own while keeping close enough to the spirit of earlier variants?

Re: the Bible, I once saw a bumper sticker that read, "If it ain't King James, it ain't the Bible." I didn't understand what that meant until I read one of those awful, 'modern' translations.