You are right, I keep all the fat when shredding a butt. I love the flavor. If I do a whole shoulder with the hide on one side, I do throw away the hide after it has finished cooking and when I am ready to shred. I am using 'shred' instead of 'pull' because it seems a few folks sometimes get confused when we use the word 'pull' and think we are referring to taking the meat out of the smoker.
Anyways, some folks might want to make cracklins from the hide (skin).
