Three of us got the rat king in a Nightfall run on Friday. Our friend still needed it so we ran a Nightfall yesterday and it didn't work for him. The other two fireteam members had it in inventory. After coming to these forums we decided to give it another go with one fireteam member having it actually equipped for the end boss fight. That worked and our fireteam member who had the quest completed it. The chain does seem buggy and the gun is very proximity based. If you are helping a friend give it a try where one of you who has it done already has it equipped to see if that gives it to the remaining member still on the quest.