We southerners are all very familiar with Piggly Wiggly. I too am surprised that the chain would be in Wisconsin. PWs do sell products that make money in their areas. Publix, etc., don’t tailor their inventories to local tastes so much. Winn Dixie does a little better at that but PW is the most sensitive to local tastes.
Simple answer. Piggly Wiggly is a wholesaler; their stores are independently owned.
Publix and Winn-Dixie are both chains -- owning both the wholesale and retail functions.