They have a natural AC of 12, in 5E, which is the equivalent of wearing leather armor (just like regular wolves, who instead have AC 13 because they have higher Dex).
Why can't that equate to the Unarmored Defense mechanic? Because it doesn't. That's not the process by which the game rules convert narrative into mechanics. The correct and consistent translation would be that they have the equivalent of leather armor. If you claim that the given narrative equates to whatever mechanic you want, then you are cheating the system, by changing the way it converts narrative into mechanics.
Rubbish!
It is not part of this ruleset that ANY and EVERY creature that, conceptually, has a higher AC through the concept of a tough hide MUST realise that concept with
exactly +1 to AC, just like leather armour!
The way it works is that the concept of tough hide adds a mechanical bonus to AC based on how tough the hide is. And guess what? The barbarian's unarmoured AC gets a bonus to AC depending on how tough the barbarian is, mechanically represented by his Con bonus.
It's not rocket science!
A game system isn't just a set of pre-defined classes that have pre-defined mechanics tied to their pre-defined narrative existences. A game system is the whole language by which a narrative is converted into mechanics. The type of hide which a wolf has is translated into a specific mechanical bonus, and if you alter that translation without altering the underlying narrative, then you aren't even playing that game anymore.
Really? If I statted up a werecreature with +2 rather than +1 of its AC coming from its tough hide, then I wouldn't be playing D&D 5e anymore?
Even the relationship between 'wolf' and 'werewolf', which conceptually gives a human wolf powers, does not result in the werewolf having an identical stat block to a normal wolf, especially in hybrid form.
Where did the hybrid form come from? The normal wolf doesn't have one! You are messing with my world by telling me how wolves work in my world!
...or could it be that wolf->werewolf isn't an exact match, that the wolf
inspires the werewolf abilities?
Y'know, just like the werewolf
inspires my barbarian abilities! Of course his abilities don't map exactly! That's because he's not an actual werewolf, in the same way that a werewolf is not an actual wolf!
Just because those mechanics could be tied to that new fluff, if you really wanted them to be, that doesn't mean they should be. If I'm being honest with myself, then there is probably a better (more accurate and consistent) set of mechanics which would better represent that new fluff.
Let's say we have a perfectly RAW D&D 5e PC. If we gave ten game designers a pure fluff description of what our PC can do, no game mechanics or class names mentioned, and then asked each game designer to invent 5e game mechanics to match that description, then they would produce ten different sets of game mechanics. They would not magically produce One True Way ten sets of identical mechanics!
The idea that 'tough hide' as a concept will ALWAYS translate to exactly a +1 AC is absurd! Proof exists in the 5e MM itself, with different AC bonuses for different creatures all based on the 'tough hide' concept.
Going back to the 'lines of demarcation' (yes, we all acknowledge that the game is all about cooperation! We don't disagree on that!), while the DM can always say 'no' to ANY part of any PC, the player can always say 'no' to playing a concept, class, mechanic or fluff that they feel has been changed too far from what they want to play.
If they cannot agree, then there is no game! Both player and DM know that, hence the cooperation.
I've already said that the DM can refuse some element of a player's fluff, and that the DM should have a rational reason for doing so. When you have a warlock patron, which according to the game rules is powerful enough to grant 9th level spells and astonishing abilities like Hurl Through Heck (I don't want to get censored

) but no patron's powers are fully defined, then it makes sense that they have power to do all sorts of things. Have you
really already established that in your game world the fiend has x, y and z powers but
definitely cannot mess with conception....
before I told you my fluff? Really? Or did you decide,
after I told you the fluff, that one thing the fiend cannot do is mess with conception, just so you feel you have justification for saying 'no', when you could more easily have just gone with it?
No, what you did was invent a reason to be unhappy about it.
We know that it is impossible for any detailed backstory written by a player to avoid mentioning people, places and/or events in the game world, things that are
usually in the DM's purview. If the very fact that the player is using those things was a valid reason to refuse that fluff, then EVERY SINGLE PC would be refused on that basis, that the player is demanding control of NPCs, places or events in the DM's game world! There could be no PC backstory EVER! The DM would create the backstory for EVERY PC, simply because the players don't have authority to create NPCs, locations or events in the DM's game world.
This would mean that EVERY PC would be a DM created handout, with no input allowed from the player. But, although playing with such handouts is occasionally done, is this the expectation of our hobby? Is it weird, strange, or against RAW for players to create their own PC's backstory?
Even in games where players use DM created pre-gens, in my experience the players are
encouraged to customise said pre-gens. I simply don't recognise our hobby in terms that players aren't allowed to create their own PC's backstory!
Of course there are extreme examples dotted about the world of players voting for abilities, DM pre-gens, DM-less games, and all sorts of strangeness, but when I talk about 'the consensus' I'm talking about the way the hobby is
usually played, the way it is generally
expected to work. And that way is that players make the choices, in play and backstory, for their own PC, and the DM controls everything else.