champions walking over a quest building show a message "Only your sovereign is allowed to do these quests" or something like that, so it seems that only the sov is allowed to pick up some rewards, but even my sov walked on a quest tile without triggering anything - I assume the quest picture was there but the quest was gone, sometimes the game shows things that are no longer there, and sometimes it doesn't show armies that are there

also the AI knows how to rob you, defeat a monster with your last movement point, if an AI champion is near, s/he will take your loot, maybe this is a way to avoid AI champions from robbing you of the most powerful items

as you say, some disclosure would help