...or can Sims donate their finds to the museum.
Yeah, that's what's supposed to happen. You get a list of items in your inventory similar to what happens when you click a plant and choose Fertilize with... Rocks and relics, maybe other things, I don't remember.
When you pick something that item appears on display. I don't think there's any particular benefit from doing it, it's more like a gimmick probably. If you regret the donation you can just take it back.
I have clicked several of those donation things on the second floor of the museum without any problems but I may not have hit the same one you did.
I've also seen them in Egypt outside a tomb.