The Asphodel Meadows in Greek Mythology were the underworld home of the indifferent.  In Welty’s story, Asphodel is a ruin whose one time occupant, believed to be dead, is spotted alive, ancient, naked, and herding goats.  Don McInnis was an unfaithful husband.  That probably qualifies him as among the indifferent.  The three old ladies who tell the story of his marriage and supposed death through their conversation are picnicking at Asphodel.  That and the goat herding probably qualify it as a meadow.  So in this story we find a quirky little tribute to the Greeks.  Classic.