The question is wrong. The earliest version of "Barbara Allen" is now in Scarce Songs 2 on my website (www.erols.com/olsonw)

Barbara Allen saw his on his death bed, but had never seen him before, and she didn't live in Scarlet town, he did, but he was obviously buried in the town where Barbara Allen lived, wherever that was! The two ballads preceeding "Barbara Allen" on my website are earlier and somewhat less silly versions of the same plot.