I'm not sure if the Playboy black/pink on the right had one and it came off with the inner (common occurrence) as there looks like a ring mark there in the centre but maybe not.
I think that there were some that were attached slightly differently and (for instance the left one as a guide) the brown part would have been attached to the metal instead of just the "hidden" part but can't seem to recall which ones offhand, sorry.
They were susceptible to the outers cracking which then usually broke in the chipping machines hence the centres falling out but there were others that you could just "pop" out and back in again easily enough, crack or not. That was a favourite thing for bored (human) chippers to do, mainly to annoy the dealer. I think that they just loosened when they felt like it and probably the more they were in use.