Does it make no difference, then, who would be doing what for whom -- giving versus receiving a pound of silver, say -- or what the consequences are, or the relationship prevailing between the parties? Is it as easy to intimidate an Elder Titan into subservience as to get patronage based on acceptance of one's own services in pursuit of some goal of the Titan's?
Is it really the case that even such basic parameters of the situation are totally subject to GM discretion, or rather dictation? Do the players in fact have no control even over the goals of their characters' interactions with other characters?
I'm not entirely sure what sort of response you're looking for, because I know from some of your other recent posts that, while you pretty clearly prefer traditional D&D play, you are also familiar with other RPGs of the sort that I have called "modern".
So maybe it's helpful if I say that I'm thinking of conflict resolution mechanisms like skill challenges in 4e, or HeroQuest's conflict resolution mechanism. I pick on these two because I know them both, I play 4e regularly and they're both authored (in part or whole) by Robin Laws.
To start with HeroQuest - the GM sets a numerical difficulty for the challenge based on the pass/fail cycle - that is, the more the PCs have succeeded on recent challenges, the harder the difficulty of the current challenge. This is an expressly metagame logic governing encounter design - the game rises and falls according to the logic of dramatic pacing. The causal logic of the ingame world is constantly adapted to meet this metagame constraint.
Thus, once the GM has set a difficulty, the GM then narrates circumstances of the challenge that (within the imaginary world of the game) establish the existence of that challenge having that degree of difficulty. The players then meet the challenge by explaining how their PCs use their abilities to overcome it. If the GM agrees that what the PC has described makes sense within the gameworld, dice are then rolled to resolve the challenge. Those dice rolls can be modified based on metagame considerations - if I try to bribe the Titan using my "Persuasive personality" ability I will get a penalty compared to my comrade who has the more focused "There's no palm I can't grease", the logic being to encourage players to give their PCs more focused, flavourful abilities. Those rolls can also be modified based on ingame considerations - I can augment my attempt based on abilities (eg if I'm bribing, I can augment with my "Sackloads of silver" ability) or based on earlier plot points (I may have earned a "plot augment" eg learning the magic word for persuading Titans). The number of dice rolls actually required to resolve the conflict depends upon whether the GM decides to run it as a simple or an extended contest - this does not affect the mathematical difficulty of success, but does affect the time required to play out the encounter, and hence the amount of story development that will take place as the encounter is resolved. The GM should make the decision about simple vs extended purely on the basis of metagame considerations of dramatic pacing.
Because HeroQuest has no money-management rules of the D&D sort, the difference between bribing and intimidating is all about PC abilities and hence the sorts of actions that PCs attempt, rather than about the risk/reward trade-off of spending money for a better chance vs saving money and trying for an intimidate.
The GM's express authority over framing - ie the GM has final say on whether or not a PC's action is feasible within the gameworld - might seem to give the GM an excessive degree of power. I think that in practice the mutual understanding that the GM's role is to facilitate an exciting adventure, and that this authority is only to be used to enforce basic genre considerations (which the rulebook discusses in some detail) ensure that this is not the case.
A skill challenge in 4e plays out a bit differently from this. The difficulty of the challenge is in part a function of its level (this sets numbers that must be achived via dice roll + bonus), but it also depends upon the stipulated complexity of the challenge, which sets a number of successful checks that must be achieved without suffering more than 2 failures. The GM therefore has two dimensions of discretion in setting the difficulty. The rules are a bit obscure on how a GM should do this, but I tend to use level of a challenge in the same way as level of a monster or a trap (it reflects its "toughness" relative to the PCs) and use complexity to reflect its centrality to the storyline - the sorts of actions the PCs will take to ensure success at a more complex challenge (eg aiding another) guarantee that it takes longer to resolve and soaks up more of the time (and hence the story) in a session. D&D 4e ultimately leaves it is up to the GM to set the complexity of challenges in such a way as to maintain dramatic pacing (it is not built into the rules in the way that HeroQuest does it - DMG2 tries to merge the two approaches, but in my view without fully succeeding). While there are mechanical features of the game that allow complex skill challenges to be resolved without a hugely lower numerical likelihood of success than simple skill challenges (such as the afore-mentioned aiding another) the presentation of this part of the rules - especially to players - is probably the single weakest part of the D&D 4e rulebooks.
The skill challenge mechanics allow for individual checks to be Easy, Medium or Hard (at level 1, that's 5, 10 or 15 required on d20 + bonus - the Easy numbers go up by half level, the other numbers by 2/3 level - the difference in these rates of escalation reflect peculariaties in D&D 4e between the rate of expected improvement for PCs' untrained vs trained skills). Difficulties are set in response to the players explaining what their PCs are doing, and the dice are then rolled. The GM is the final arbiter of the degree of difficulty for any given check, being encouraged to factor in both ingame (is it plausible?) and metagame (is it cool?) considerations. So sweet-talking a Titan might be easier than intimidating it.
The rules are not entirely explicit, but I think it is assumed that, as in HeroQuest, the GM has final authority on whether or not a player is allowed to have his/her PC attempt a desired action. The rules also imply that this authority should be wielded lightly, and that the preferred response is for the GM to set higher difficulty numbers for more outlandish attempts, provided that they don't violate the basic genre parameters of D&D high fantasy.
The DMG2 has some suggestions on how to account for bribes - if the bribe value is at least 10% of the value of a magic item of the challenge's level, it gives a +2 to a skill check. The rules don't deal comprehensively with all the other considerations one could think of, but (for example) a promise to give onself over into slavery to the Titan would probably be worth at least an automatic success, mabye two! D&D 4e doesn't handle some of these issues as well as HeroQuest because things like money, items and one's status as a slave operate outside the skill system, whereas in HeroQuest these are all simply character abilities, and so are integrated into the core mechanics of that game.
Attempting a summary answer to your questions: yes, the players have control over their PCs' goals, and yes, whether the PCs interests align with or conflict with those of the Titan matter,
but the game mechanics establish parameters within which the players can
know that, provided they can plausibly frame their PCs' response to the scene, their is a game-mechanical process they can follow that can allow them to succeed in their social endeavours. In this respect, the skill challenge rules bring social encounters in D&D 4e closer to the combat rules (in HeroQuest there is no mechanical difference between combat and other forms of conflict resolution).
The interaction between the GM's initial framing of the encounter, and the players' choices about how their PCs respond,
combined with the fact that the rules require this to be driven to resolution via a dice roll, also impose shape to these encounters which I have found harder to achieve using the traditional approach. In the session I GMed on Sunday, for example, there was a negotiation between the PCs and some duergar slave traders who had purchased, as slaves, the villagefolk that the PCs were hoping to rescue. As the players narrated their PCs' skill checks - at some points Diplomacy, at other points Intimidate, and culminating in an agreement involving the drafting of a contract and the establishment of a trust fund - the encounter evolved in interesting ways, with interesting response on the part of both the NPCs and the PCs. This was entertaining to both players and GM. I've found it harder to get this sort of dynamics into social encounters using the traditional approach, because that approach puts more responsibility on me as GM to decide when and how such dynamics occur. The "modern" approach gives the mechanics - the dice - a more central role. This is another respect in which 4e social encounters are more like combat.