Yes (I'm back, sorry) Shop Rite is a Co-op. Wakefern Is the parent buying entity, Wakefern is made up of MANY Shop Rite Owner Groups who have autonomy over their individual store groups , but try to come together (and they do very effectively) to ban together and create scale and limit competition .
To answer your specific question. Boars head has specific criteria by which they will sell. or NOT sell out. Wakefern years ago said "ok...we'll establish out own Private Label Brand".....hence the birth of Black Bear. Get it?
You may still see some geographic brands on shelf across the owner groups. But in general Wakefern drives the bus.
They remain a MAJOR player in the NJ/NY Grocery business and have survived and thrived while most have not. They have beaten back Grand Union, Acme, Stop n Shop, A&P, Pathmark, Foodtown, Wegmans, and Walmart and Target......leaving Kings to bite at their ankles (although they actually supply Kings now too)