Can you do it?
The examples my friend brought up are when you have options available to an entire detachment, such as Salamanders being able to upgrade 1 weapon on any character- does this allow Salamanders Unique Characters to Master Craft a weapon they are equipped with? Or can any of the named Alpha Legion Unique Characters in HH Book 3 be upgraded with a power dagger, as it says any Alpha Legion Character can be upgraded with one in addition to their normal weapons?
I think this should be no, and I feel there is a line somewhere in the rules that prohibits it, but I can't find it. I'm certain it was there in earlier incarnations of the rules though. It is possible it has been omitted in the 7th edition iteration though. Certainly RAI I think it shouldn't be allowed.
EDIT: I don't mean situations where the upgrade is explicitly stated in the Unique Character/Units datasheet/entry (such as Marneus Calgar upgrading to the armour of Antilochus), but ones that would usually apply to the army, which technically also seem to allow Unique Characters.