Hamlet Questions (full loot lists and effects of provisioning?)

[Bebekurenai]

Having a provisioner in your party gives youa boost in points and allows for tradebale Crafting or Gathering drops to come from the NPC at the end to the provisioner. There is a chance that an untradeable Gathering hat may drop into the party loot.

3 out of the 4 gathering hats that i have seen dropped were dropped on 50k runs. people have said that 70k runs do not drop the 100% hat so they might have a separate loot pool

Does this mean, hats will only drop when a provisioner is present? We have done so far 150-170 hamlets, and maybe half of them when not more, with provisioner, always over the 60k mark with ot without prov. Not a single gathering hat has been seen yet. Any particular condition to make it drop?