The mechanics directly change the fluff. And you're also missing out "This fight is on a cliff edge" - a nice piece of fluff. No representation for that in DiTV under anything other than extraordinary circumstances.
This is completely and utterly not true.
If we're having a fight on the edge of a cliff, that fictional aspect is most definitely important to the conflict. It matters because fictionally I can use the cliff. I can push you off. That directly makes an impact on the mechanics: the fallout I take - as GM I'd probably rule this d12s, akin to dynamite or something else serious like that depending on the size of the cliff. It could also factor into play fictionally/mechanically if someone has a trait related to cliffs (Scared of Heights 3d4).
If we're not on a cliff, I can't do that. I simply can't. If we're in the town square, I cannot push you off a cliff. Period.
So, it's very important to the fiction and mechanics of the game.