PG56 BAs codex under wargear
"Weapons and equipment that can be used by more than one type of model or unit are detailed here, while equipment that is unique to a single model or unit (including wargear carried by a named special characters) is often detailed in the appropriate entry in the angelic host section."
The Axe Mortalis... detailed in the angelic host section under a special character named dante.
Grey knight codex says a similar thing, and cites Crows sword as unique, even though its just a CCW.
Space marine codex as well, pg 97
imperial guard pg 29
codex dark angels pg 48 same thing
I think that makes it pretty clear that in the case of GW and warhammer 40k, they define "unique" rules for a weapon as being listed in a unit entry specifically with a unit in a codex. The actual rules it has doesn't matter only that its listed with a unit in the unit section. Looks like a case of the game designer using game jargon that players might not use.
Thats why The blood crozius was amended because otherwise it would have been a "unique" power weapon.
Your mixing the issue now. Nowhere in the rules for either Force or Power Weapons does it mention "unique weapons". They mention "unique special rules".
Dante's Axe (since it keeps coming up) is a "unique weapon" (being a named weapon belonging to a Unique Character"), individualized to Dante. HOWEVER, it does NOT have "unique special rules" thus does not get lumped into being an "unusual power weapon".
It's clear that the Developers didn't mean "unique weapons" or "weapons belonging to unique" units when there are NON-Unique models affected by these rules (because you know, they may have decided to use those phrases rather than "unique special rules").
To give you an example of why your interpretation doesn't work: The Mistress of Repentence for example is a NON-Unique Model but she has Unique Special Rules on her Neural Whips. If the rules for Unusual Power Weapon didn't extend to cover NON-Unique models, then there would be no classification for her weapon as it is a whip (note the lack of entry for whips). THAT would be in direct violation of the fact that ALL power weapons fall into one of five categories.
You keep trying to turn this into some kind of solution where you get to be right on this one. Here's a hint: unless you change your point of view and agree that Unique Weapons aren't IMMEDIATELY "Unusual Power Weapons" just because, then you'll still be wrong. The ONLY way you'll be right is if GW puts into the FAQ/Errata.