Short and Sweet:
Make a clarification tab pop up, the same as binding equipment now, when passing loot to another player in a chest.
It's very easy to misclick and pass the item to the wrong person. Now you may say who cares, majority of people are considerate enough to pass to the proper person anyways. The issue comes up when some of the people leave the quest before the passing occurs and the loot is accidentally passed to the wrong person.
An even better way to do it would be to make it pop up for the person who would be receiving the item. If they do not answer within 10 seconds then chances are they've already left and the item remains in the original person's name.
Save the disappointment!