I haven't messed with mine in a decade now. Think that liner just rides in there to limit popping wheelies? I'd have to look that one up. Give the disk a little slide before it grabs and goes? Definitely not glued. Don't remember that at all. Snapper doesn't make cheesy junk that needs to be glued.
When we were a dealer, the smooth-start clutch liner was indeed glued in place. There were two different part #s, one for the "wheelie" mowers and one for the smooth-start. I think that later on, the aftermarket just used one disc for both and you installed the liner. I don't know if you glued those or not, since they weren't around in my era.