This looks to be fixed??? I was able to complete it and saw someone who had no loot able to complete it too!
I just abandoned the quest, re-aquired the quest and then it worked 3/3
Went away and did other things for awhile, came back and they are lootable. Hopefully that means it was hotfixed and working for everyone.
First time for me as well and it’s bugged.
I can confirm that this morning, I picked up the quest again and was able to open all three chests successfully and complete the quest.