My point is, skills is what you need to do enough mystery for it to work. So I think the answer is more "you can do mystery" than other genres.
For D&D? Sure. It does mystery "better" then it does drama (though it does both poorly)/
You're missing my larger point.
Let me rephrase using a different example. Take say... our perennial favorite: Vampire.
Vampire CAN be used to tell stories of personal a personal decent into horror and darkness. It's got a humanity trait. It has horribly crappy mechanics to use that trait.
It's not a good game to tell this kind of story in, but you can use their horrible mechanics to do it WITHOUT FIAT RESOLUTION. The rules are there. They are poorly made, obnoxious, and difficult to use, but they do exist.
This is similar to using D&D to tell a mystery. You -can- do it, you can even do it without fiat-ing anything, it's just not optimal. Other games do it better.
Our disagreement here appears to be that you believe that poorly done, or poorly fitting mechanics don't count AS mechanics when used in sub-optimal ways. In D&D you can achieve the same resolution of dramatic situations as Burning Wheel's duel of wits through the use of contested Persuasion rolls. You find out who persuades whom through die-rolls.
Does it do compromise? No.
Does it decide everything through one die roll? Yes.
Does D&D lack the "let it ride" rule making multiple rolls until you "get it right" annoyingly probable? Sure.
It's a sub-optimal alternative, but the mechanics exist to support it. They count. They are not fiat.
You might not like them (I don't), but they do exist, and their existence complicates the chicken+buttocks equation. Sometimes fake chickens are better then real chickens because they are so much less expensive. Sometimes using a sub-optimal resolution system for a specific task is better then spending the energy necessary to convert to a more optimal system.