I've heard that one, but a long time ago, and I've forgotten where.
If Samuel Pepys' diary hadn't mentioned the song, we would have to take "Barbara Allen" to be a reworked version of "The Ruined Lovers", of 1684-6, in my broadside index, ZN1756, which has the same (rather slight) story. This is a few years earlier than any known copy of "Barbara Allen"