I think you had it right the first time. I can't count the number of imaged I've seen of Adams with his Stetson, and do recall one image of him using it as a shade with hid 'blad. Weston on the other hand more often than not seems to have gone "lidless". I can only recall seeing two shots of him with a chapeaux - a Campaign hat and a beret. In his list of equipment for his Guggenheim, he always seems to mention the "Worsching Counter Light Cap" a combination lens shade/lens cap.