Rolls are abstractions of actual in-game events. One of the jobs of the DM is to read those dice and determine what's going on in the reality they represent. While I'm part of that faction who believes that the dice rolls should represent some measure of reality in the setting, directly related to the actual game-reality. That is, I dislike high levels of abstraction in my games—but by that same token (the token of abstraction) I admit that some level is necessary for ease of use and speed of play.
The gap, the great chasm between "roll to-hit" and what is actually happening in the game-reality, MUST be bridged. The shorter the gap, of course, the easier to bridge it; it is very simple to understand where someone strikes if there is a mechanic for determining which portion of the body is struck. That requires very little interpretation on the part of the GM. However, that also compounds the number of rolls and slows gameplay by a great deal (which introduces another type of "distance" from the action).
One of the things it takes to be a good GM is the ability to quickly digest incoming numbers and translate them into game reality. I don't use a system to determine what happens when there are fumbles (a "1" rolled on a to-hit d20). I simply rapidly determine the outcome; sometimes a weapon is dropped, sometimes it is shattered, sometimes the fumbler opens themselves up for a quick free riposte, and sometimes they fall to the ground. If they're up on a ledge, perhaps they need to make a Dex check or Breath Weapon save or fall off. This is all completely arbitrary because the faster I can move through the combat the more adrenaline will be flowing through the players.
The same cannot be said of critical hits in my games; I use the complicated C&T system, because we've all agreed that we want critical hits to be more gruesome but by that token I cannot bring myself to arbitrarily decide that someone was struck in the knee and now has a permanently debilitating wound there. Green Ronin's Black Company d20 game actually has a great system for this as well, and both are systems that I've used.
Other important interpretation points include the hotly disputed Hit Point; when you do 8 damage to someone, the description of how bloody and unpleasant the wound is depends on how great a fraction of their total HP was taken, or how close to death they are. This is something that a DM must be able to do on the fly and with great rapidity.
The theoretical issue here is one of distance. The game-reality takes place simultaneously in the minds of every player but issues from the DM alone. Between the game-reality and the individual there is a great crack or chasm which can only be bridged by the DM, from whom information comes. In that way it is Clausewitian; there are some things players will always need clarified because of the so-called "fog of war" between the players and the action. To make that gap as small as possible, to bring the game-reality into the room, is the job of DM. The better your DM is, the more the world of the table dissolves and you find yourself in the world of the game.