Interesting...
I usually do quest events with 2 other friends. When 1 friend shares a fetch quest, the other 2 accept it as normal. After the one who shares it activates the quest rally point we all locate our own separate satchel in the same building as there are often 3 - 5 scattered around depending on the size. Sometimes we may all have to go to the same satchel but not often as they seem to be set randomly for each person in the quest party. We don't leave until we all pick up our own separate satchel as those who don't collect it will fail the quest when you move 25 meters or so away from the building. Is it not working that way for you?