In the absence of a clear ruling, I'd bet that most groups use "the real world" as the "independent arbiter" for how our characters experience the fiction.
I suspect something close, but different. I think most groups use the way they
think the real world works as a model in the absence of any clear rule - or in the presence of any rule that superficially clashes with how they believe the world works - as an "independent" arbiter. Part of the problem is that how a player believes the world works is not really "independent". Using how the real world really works is not a viable option, sadly, as no-one has the source code...
A player saying "The rule doesn't really work that way" is actually a player saying, "The result you've just described doesn't fit with want I want / believe / expect from the fiction your game portrays."
Right - it says "I have a preconceived notion of how this game
should play, which I think should supercede what the game designers wrote". It's an approach I think is inferior to "well, let's see how this world worked according to how the designer (apparently) saw it - if we don't like it we can always change it or just choose a different game".
Associated mechanics are easier to GM in disputes because they ultimately point to some real-world, causal phenomenon that either permits or prevents the described fiction from working.
I have yet to see a "dissociated" mechanic that doesn't nod towards a range of possible genre trope or real world explanations for what is happening; the "associated" ones just seem to point more explicitly and narrowly to a specific cause or process that is supposed to be what causes the effect every time. This very "sameness" of cause is something that I (and, it seems, several others) find difficult to believe in itself.
Obviously, both the players and GM have to agree that the "real-world" cause is in accord with the fiction.
I don't honestly see that they do. If everyone agrees that the resolution of the action is what it is, then if different players have envisioned slightly different ways that it came about - ways that they individually find plausible - then why is that an issue? If we all agree on the resolution, then we can all synchronise our world models with that resolution in place. We don't
need to visualise the same route there in every detail; in fact, if we go to minute enough detail, that would be impossible to do.
A more serious charge would be that the outcome or resolution is unclear - that the players are unable consistently to envision "how things are" as a result of the mechanical resolution. Something like "Schroedinger's hit points" would qualify. It seems to me, though, that at least part of the issue here is players wanting to know precisely the "real" state of affairs at all times, when some uncertainty would be (a) more dramatic and exciting and (b) entirely plausible in the situation.
Take the case of the character being unconscious in 4e. They are making death saving throws to avoid dying. But, then, a leader spends healing resource on them and they get up and are ready to fight again. Is this plausible if they had a grievous wound (and, maybe, the healing wasn't earmarked "magical")? No - but nothing said they had a grievous wound, just that they were on the deck. Maybe they had a killing wound - maybe they didn't. In the chaos and confusion of combat, that's just something you don't get to know until later. Ambiguity and uncertainty are part of any stress situation - and they are part of what makes it exciting (for the audience) and terrifying (for the participants)!
Associated mechanics ultimately protect both the player and GM better, because disputes are more easily resolved using known, experienced processes.
How many gamers really know and have experienced hand-to-hand fighting with medieval weapons? Never mind the added presence of magical effects, impossible monsters and the simple fact that they are not in the "real" world. As I have learned more of medieval combat alone, I have come accross multiple cases where "common sense" is just plain wrong. Studies of safety incidents on industrial plant (something I have done as part of my job) shows me similar things about general "crisis" situations. The problem is that we like to think that we know and understand these things - but we really don't.
In itself, that's not a big issue - the game world is not the real world, after all, so there's no reason we can't have it act just the way we want it to. The problem starts when different experiences and degrees of knowledge mean that different people at the table have models of "reality" that differ markedly at several points where the game habitually goes. Like "crisis" or stressful situations, catastrophes and combats.
Mechanics have three recourses during a dispute---the GM puts his or her foot down and says "No," the GM basically has to say, "Well, that's what the rules say, even if I don't like it," or the GM is forced to make a snap judgement about the nature of the fiction itself.
Or make a pro-tem ruling, preferably in line with the rules, since that is what people (ought to) expect, and then discuss it as a group and decide whether it bugs everyone enough to make a house rule.
The rules aren't the stuff written in the book - the rules are the precepts and procedures you play by. Changing the rules instantaneously mid-stream is not really cool, whatever way it happens, but changing them with everyone buying in is entirely reasonable. It's even reasonable, for some groups who have an unwritten rule saying "no matter what the game rules say, our game worlds always work like this", and they alter any rule in the game they are playing to fit their set of "over-rules". I think that is a boring way of playing, personally (every game world you play in works the same way), but if some groups want to play that way I see nothing wrong with them doing so. This is one reason, I think, why it's hard to discuss this without feathers getting ruffled. If you are part of a group that has a "default world assumption set" then you won't see the issue with "changing rules mid-session" - because
your rules aren't really being changed mid-session, you are playing to the same rules you have always done when the DM says "well, of course, trip doesn't work on oozes, as we all know..."
People come to the game with prior conceptions and models of what a fantasy game-world looks and feels and behaves like. They don't get all of this from the game itself. The coordination of the participants' separate conceptions and models may be a major function of the rules, but the rules are not a major contributor to this coordinating process. Most of it is just talking and having a shared cultural background.
Of course people have their own views of how each game-world looks and feels. They don't even need to synchronise these views completely - indeed, it would be impractical to do so. But they do need to synchronise their understanding of how outcomes in the world arise - how interactions between their character and the rest of the world are resolved. And they get that understanding from the rules, whether those rules are what is written in the book or are an agglomeration of understandings and shared assumptions built up among the group members. Of these sources, one has to assume that the rulebook takes precedence unless otherwise agreed - otherwise, what would be its purpose?
Why must a trip and a throw be defined the same way?
Does it hurt the narrative (or the story) if trip and throw are two different options which each have strengths and weaknesses?
I don't think it hurts the narrative either way (defined as two separate mechanics or one abstracted mechanism), but it hurts
the rules if they have to be defined differently in every instance. The rules system either becomes bloated and overcomplex through a multiplicity of subsystems (for trip, for throw, for induced missteps, for faking out...) or it remains horribly constrained (you can try to trip, but aren't allowed to throw, induce missteps or fake out an opponent...). In short, the best way to get a varied and flexible world is by having flexible, abstract rules.
Does it hurt the narrative if fireball and lightning bolt behave differently?
I don't know of any rule system in which they both exist where they don't behave differently - what would be the point in having both effects if they were exactly the same?