Do all unique items have fixed parts?

I have played my first 15 hours of co-op and every red text item we got from quests or fixed drops have been identical except for in some cases there level.
It makes me wonder if this is true for all unique weaponry with flavor text or is this just for fixed drops/ quest rewards so we do not need to farm quest rewards for attachments or prefixes. Regardless I like this change so far as it streamlines farming for a good amount of loot.