The fantasy elements are the foundation and the core, everything builds up from there. If the setting and story conflict with the mechanics the mechanics MUST adapt because the simulation is a complete slave to the ideas it is simulating.
This, I think, well sums up the so-called simulationist approach, that the mechanics
adapt to fit the setting and story. I think what Jeff is getting at in terms of a polar approach is when the mechanics don't have to adapt because 1) They are free-form and loose enough to "bend" to whatever situation arises, and/or 2) The default approach is one of ad hoc decision making and "handwaving," not finding or creating a relevant rule.
In some ways I think this comes down to a matter of different temperaments, which could be characterized as
Dionysian and Apollonian. When a conflict of story and rules arises, the Dionysian approach is to either ignore the rule or over-rule it with DM Fiat, in favor of the story. The Apollonian approach is to adapt the rules or create a new one. The Feat system that both 3E and 4E use is the embodiment of this more Apollonian simulationism: Want your character to be able to do something? We have a feat for every occasion and if we don't have one we'll make another up. The Dionysian free-form approach says: Want your character to be able to do something? Sure, he can try, so make a roll (or "Sure, just write it down and we'll figure out how it works").
The thing, though, is that very few players and DMs are at one extreme or the other. Sure, we've all met diehard Dionysians--this is where we get the lightest of "rules lite" games, Amber Diceless, Everway, etc. And we've all met diehard Apollonians--they tend to have huge binders of house rules or play GURPS or Rolemaster

. But most gamers are somewhere in-between, on the spectrum, so to speak.
I do think it is safe to say that the locus of D&D has moved from "left of center" to "right of center" (if Dionysian is left and Apollonian right), with 4E moving slightly back a bit left from 3.5 (emphasis on "slightly" and "a bit").
For me the Holy Grail of D&D would be a design in which the entire spectrum is served, because all approaches are valid, all styles welcome within the D&D Family. You want to chart out Demogorgon's skills and feats, down to how well he can shine shoes and throw a bola? Fine, go right ahead. You want to bypass all feats and powers in a completely free-form approach of character actions? Sure, why not?
Some would say that a game that tries to please too many masters, that tries to be too many things, loses its vitality. This may be true, or at least it is
easier to make a more tightly focused game of quality, but I don't think it is something written in stone, that a single version or edition of D&D has to serve only one sub-set of the total D&D population. You're never going to please
everyone, but like Zeno's arrow I think you can continue to halve the distance infinitely.
At the least, why not die trying? To paraphrase a famous quote, "I'll give you my dice bag when you take it from my cold, dead hands!"