It's a re-opened dungeon, so if you completed them previously (when Beast Eddie became available) then you won't get the first time rewards again.
I understand your logic, but I don't think that is what was intended. I think it was intended for us to get set rewards the first time we pass any difficulty level of the dungeon this time.
druid138-6195
Sunrise Senjutsu Eddie Pity me none
at the gates of our hell