The DM narrates a situation and the players have to react to accommodate it. It doesn't work the other way around; the players do not tell the DM that they want to find a magic sword in the cave and the DM must react to accommodate them, for example.
A quibble - in the 4e DMG, there is an expectation that if a player tells the GM s/he wants her PC to find a magic sword, the GM will provide it, if not in this cave perhaps in the next cave along.
But otherwise, I tend to prefer a game in which the GM exercises primary control over scene framing. That doesn't mean that I completely disagree with LostSoul, however.
it still falls upon the DM to provide the plot and the setting.
I dont' really agree with this. I play a fairly traditional game where I, as GM, have primary responsibility for the setting. But the players are able to introduce plenty of setting elements themselves, both via PC backstory and in the course of play. And as far as plot is concerned, I very much prefer that that emerge out of play. I don't want the GM to provide it (either when GMing, or when playing).
I am not interested in playing through an Adventure Path. Neither am I interested in playing through a DM's pre-plotted campaign
I don't want to experience the DM's story, so I don't play in those games.
I don't mind a game with a strong initial situation - in fact, I like that, it gives me some guidance in character creation - but I don't want the DM to have any preference as to how the campaign will play out.
I'm not interested either in GMing or in playing Adventure Paths, nor pre-plotted campaigns. I quite like strong initial situations, though my own approach is to escalate the situation as the campaign progresses - I tend to find that this fits well with the general thrust of traditional fantasy RPGing, with the scope (thematic, geographical, metaphysical) growing as the PCs gain levels.
I must confess that I do have preferences as to how the campaign will play out, at least in the sense of having aspects of the PCs that I find interesting and want to push harder. That's not necessarily a preference as to plot outcome, but is a preference about thematic and genre content, I think. And to put up a negative example: I have a player who is into military history, and wargame-y board games, and would really like to play out an extended war scenario. Whereas I really don't want to run such a game, and even when he tries to build in hooks and prods to take the game in that direction, I as GM repeatedly fail to bite.
Luckily for both of us, the same player also enjoys the mythic history aspect of fantasy RPGing, and the scope that creates for a PC to be connected to the various metaphysical factions and their plots and schemes and conflicts. And this is stuff I also really enjoy, so I follow his leads in this department instead.
I want my choices to have an influence on how the situation unfolds. If the DM wants the situation to unfold in a certain way - and, I guess, takes steps to ensure that happens - then my choices aren't influencing the situation and there's not much point in me playing.
For me, it's the "taking steps" that is crucial. But "unfold" is also interesting. If, as GM, I find some aspect of a PC that the player has introduced, and started bringing out in play, interesting, then I might design an encounter or situation that tests that aspect somehow (simple eg the player has the PC expressing frustration at a lack of power resulting from following the gods' prescriptions; I might have an imp or quasit turn up to make an offer of an alternative path to success!).
That's my interests, as GM, making me take steps to have the situation unfold in a certain way - ie how does this PC (played by this player) respond to temptation. But I don't think it means the player's choices are failing to influence how the situation unfolds. It was framed in response to earlier choices they had made, and creates room for them to make new choices that will affect the framing of future situations.
I want to be able to, through smart in-character play, control the factors CNN listed in the post I replied to.
I certainly agree that smart, in character play should affect the nature of the adversity that a PC faces. That is, it should affect the plot. I'm not so sure about what effect I like it to have on the duration, intensity, frequency etc of that adversity. As a GM, I tend to assume primary responsibility for those things, in order to keep pushing the game forward.