Actually, I've done a lot of testing here while implementing the 'Skilled Barbarian Raiders' into the RAR mod.
As usually, the rules are highly confusing

.
1) To get a certain unit from a hut, you need to have this unit enabled for your Civ (but don't have to be able to build it yet, neither technologically nor because of resources).
2) To get a certain unit from a hut, at least 4 Civs must be (theoretically!) able to build that unit. The oddest part is that enabling that unit with a starting tech for 4+ Civ
not in the game does work as well.
Example: Replace the Barb Warrior with Archers, and you'll get that ones right from the start even if no MIL Civ is in the game.
3) 'Being able to build it' for 4+ Civs includes
seeing the resource for 4+ Civs (but not 'having it connected')
4) You always get the 'more basic' Barbarian unit.
For mods, this means if you want a unit from huts that cannot be built by any Civ you need a dummy resource; either one that isn't on the map at all (but would be visible), or use Whales, Fishes etc (a resource that cannot be connectde ever).
For unmodded, it only matters for
Sumeria in C3C (at least, that's what I thought before this shot):
Sumeria can never get a Skilled Barb Warrior (because Warriors are not enabled for them). But, once 4+ Civs can theoretically build Horseman, they can get those (chances should be the same).
Same was true for Aztecs pre-C3C.
Now in this example:
1) Which Civ is that? Sumeria with a changed color (you can do that in the ini, without moddifying the biq)? Dutch? England?
2) If not Sumeria - do you have Iron Working, and Iron connected? Could be you do not get an obsolete unit.