how do you logically get to a conclusion where someone placing a chair in a spot they cleared is somehow relying on anonymity?

In the interest of helping you out, I'll offer this one: the people who want to save spots, can put their name, address and phone number on the item they wish to use to mark the spot.

That way, when DPW comes and picks it up, they'll know who to fine for littering.

Oh, no, that would be too much like admitting they know it's wrong to mark spots.