You're on the right path here. The items from reputation vendors do not unlock the piece in Collections. If you were to compile the set from different, non-reputation sources (such as some from the Cartel Market, some from the GTN), it would unlock. Reputation items, however, are specific to the character with the rep.
So if I understand correctly, are we supposed to consider the items from the Contraband and Bounty rep vendors (Thana Vesh set, Mask of Nihilus, etc) as the ones that are "bugged" since they do
unlock those items and complete sets on the Collections?