Dead jellyfish stings

Inspired by this thread.

When I was a kid there would often be white-and-purple moon jellyfish washed up on the shore. I never touched them, as I was an obedient kid and was warned against it.

I know that the nematocysts can still be triggered on the tentacles of dead jellyfish. But do the bells also have stingers? If I were to touch the bell of a dead moon jellyfish, would I have been stung? Or are they free of nematocysts?

I am not aware of any jellyfish species with stinging bells, so I think you would have been okay if you were positive no tentacles were lying on top of the bell.

In Key west when the jellies are in, somebody patrols the beaches in the morning with a shovel to prevent people from stepping on one.