So I joined a quest already in progress, get to a chest that had already been looted before I joined, so of course there was no loot assigned to me. Just out of curiosity I clicked the "re-roll loot" button at the cost of X astral shards. Well, the game happily took my shards for the re-roll and the chest remained empty.

Therefore

There should be no "re-roll loot" button on empty chests / chests that were looted before your character entered the quest.