Interesting - I might be missing the mechanical difference, but can I ask:
In the "loot 3 weapons" quest is a roll of "objective item" on any treasure table treated as a weapon? Does it make a difference if the treasure table roll comes from a monster kill, or from a non-encounter roll, such as a find or geographic roll?
I think there is a Q&A document somewhere that implies it does count, but in trying to find that to link here, I also spotted https://boardgamegeek.com/thread/2390775/article/34352541#34352541 which seems to suggest that Q&A document might be for a previous version?
That being the case, then I guess it is mechanically consistent between the "loot X of someting" and "collect two rolls from table TA", insofar as the "objective item" treasure table result does NOT give you one of the things you are seeking.
With the exception of rolling "objective item" on table TA, when you need to collect two rolls from TA. What item do you get in this situation? Do you need to roll again until you get a different result? Or do you get a "fine item" worth 100gp? I'm guessing it's the fine item, but asking to be sure.