Spooky; I don't know what purpose the cotton ring serve, but probably some dampening? What I do know is that removing the metal pins that held it together fixed my rattle. It looked kind of cheap and badly done, so I removed them and sew the ends together instead. Worked like a charm for me.
Just want to say thanks for saying this; I did the same thing and it seemed to eliminate my rattle. I didn't take the driver all the way out -- I didn't want to mess with the silicone if I didn't have to. But I did thoroughly inspect the black foam piece for any hairs or other debris and cleaned out what little I could find. That, in combination with removing the staples that were in the cotton ring (and sewing it instead) seems to have done the trick.
I was going to send them into the manufacturer (they're still well under warranty), but I figure that I might as well just keep them now that they're working well. I don't really want to be without them for a long time!
One thing I do think is strange is that I do not notice any vibration/rattle whatsoever from the left ear cup, so I didn't alter it at all. The way I see it, if it ain't broke, don't fix it. If it starts rattling, I'll take it apart and do the same thing. Otherwise, why bother?