Stress can cause picking, plus I have seen stronger birds pick weaker ones just because they seem to know they ARE weak. Also, if any were sore, red or had any bleeding from the vent caused by the illness it would have started the picking just from that. Sometimes they will even pick chicks who start to get pasty butt thinking it's food stuck to their butts.
Since spraying with blu-kote, there is no more picking - thankfully. There are a lot of obvious sick chicks since the Vicks and Oxine treatment. I hope that means it's working.