But basically there is malleability in the reality that doesn't exist in some other approaches, and that malleability is what allows a lot of the mechanics of the game to work. Flashbacks are an obvious example, but often the consequences can rely on this too. Like in our last game the location of the guards was dependent on out roll to perceive them.
I feel that this claim - or rather, the ostensible contrast that it is intended to support - is exaggerated, even for BitD.
It's quite legitimate, in "trad" RPGing, for the GM to roll a random encounter, and for the result of that roll to dictate that guards are present.
Having the presence of guards turn on a roll is therefore not distinctive to BitD.
What is distinctive is the way the rolls, and their relationship to decision-making by the participants, to framing, and to consequences, are structured.
Here is one illustration,
in relation to combat resolution:
Fortune-at-the-End: all variables, descriptions, and in-game actions are known, accounted for, and fixed before the Fortune system is brought into action. It acts as a "closer" of whatever deal was struck that called for resolution. A "miss" in such a system indicates, literally, a miss. The announced blow was attempted, which is to say, it was also perceived to have had a chance to hit by the character, was aimed, and was put into motion. It just didn't connect at the last micro-second.
Fortune-in-the-Middle: the Fortune system is brought in partway through figuring out "what happens," to the extent that specific actions may be left completely unknown until after we see how they worked out. Let's say a character with a sword attacks some guy with a spear. The point is to announce the character's basic approach and intent, and then to roll. A missed roll in this situation tells us the goal failed. Now the group is open to discussing just how it happened from the beginning of the action being initiated. Usually, instead of the typical description that you "swing and miss," because the "swing" was assumed to be in action before the dice could be rolled at all, the narration now can be anything from "the guy holds you off from striking range with the spearpoint" to "your swing is dead-on but you slip a bit." Or it could be a plain vanilla miss because the guy's better than you. The point is that the narration of what happens "reaches back" to the initiation of the action, not just the action's final micro-second.
Both methods of resolution involve rolling the dice to establish what happens, following the announcement "I attack". But they are differently oriented to what is at stake. The first narrows what is at stake to
does my blow, that I commence and that is in motion, connect? The second sets as the stakes the much more broader
does my goal, which is to take down the guy with the spear by attacking with my sword, succeed?
(Note that the reference to "the group" discussing the fiction is optional and a bit of a distraction: in Burning Wheel, for instance, it is the GM, not the group, who decides what happens, and how, "from the beginning of the action being initiated". But BW still uses the second method.)
The imagined fiction, in the second approach, is not more "amorphous". Both approaches involve the setting of the scene and declaration of the action - sword-PC attacks spear-guy. The difference is in how framing, roll, stakes and consequence-narration are established. The first approach is more "neutral", in that the narrator of consequences doesn't get to inject their own opinion/intuition/preference/taste into the narration in the same way that that narrator does in the second approach. This brings us right back to
@Campbell's comments about the difference that processes of play make, if one is looking to play narrativist. "Neutrality" and narrativism are at odds.
The combat example of course generalises to all sorts of action declarations. But let's look at a guards example.
Consider: the players declare that their PCs go to place X, and look around. The passage of in-game time prompts the GM to roll the random encounter dice. The result is guards. The GM tells the player they see guards. The GM, here, is neutral in that all they have to do is track time, make rolls, read results.
Vs, the players declare that their PCs go to place X - this is low stakes in itself, and so the GM narrates the PCs arriving at place X, which is described as (or perhaps which everyone at the table knows to be) ominous, foreboding, likely well-protected, etc. The players declare that their PCs look around, to make sure the coast is clear. The player rolls their dice. The roll fails. So the GM "reaches back" to the initiation of the action - and tells the player that the coast is most definitely not clear - their are guards, and they've spotted you!
The first approach is pretty unremarkable for D&D play, or Traveller, or Rolemaster. The second could be an example of Burning Wheel - the GM says "yes" to
we go to place X and then calls for a roll on Perception when the PCs look around, and the roll fails, and so the GM narrates failure via intent and task. It could also be an example of Apocalypse World - the GM makes a soft move in response to
we got to place X - narrating the foreboding place, etc - and then the player has their PC read the situation and fails, and so the GM makes as hard a move as they like,
putting the PC into a spot. I don't know the details of BitD very well, but I suspect from my knowledge, and from the example I've quoted at the top of this post, that the second approach could also be an example of BitD.
There is no more or less "amorphousness" in either example. But in the first, the players' main incentive is to minimise the passage of ingame time (which is a type of resource, perhaps: actions relative to encounter checks). There is no tight relationship between player goals, and what is at stake in rolls. The second example is different in both respects: in declaring actions the players are not managing a resource, and the connection between player goals and what is at stake in rolls is very tight. The focus of play is quite different.
A third pair of examples is confined to Burning Wheel vs D&D and similar approaches. Consider, again, the players declaring that their PCs go to X, and look around. The passage of in-game time prompts the GM to roll the random encounter dice. The result is guards. The GM tells the player they see guards. The GM also rolls the encounter dice, and they come up 12 on 2d6 - enthusiastic friendship! The GM thinks quickly - recalling that, as per established backstory, place X is in the home town of one of the PCs, the GM narrates that the PC recognises the guard as a childhood friend. And so the encounter unfolds . . . (On a reaction roll of 10, maybe the GM makes the same decision about background connections, but the guard isn't friendly to the potential interloper, and so the GM has the guard tell the PC "If you turn around now, I'll forget that I saw you . . . but I'm not going to let you in.") The GM's quick thinking, guided by the dictates of the reaction roll, reflect an aspiration to neutrality rather than imposing of will by the GM.
In BW, let's suppose that the players declare that their PCs go to place X, and the GM says "yes" because this is low stakes. And now a player says "I'm in my home town, I know people here. I make a Circles check: I'm hoping that one of my old friends is on guard here, so that they will let us in!" The Circles check is made, and lo-and-behold, it's as the PC hoped. Things unfold just as in the D&D-esque example with the 12 on the reaction dice. (If the check fails, maybe the GM narrates things as per the reaction roll of 10, because that is what will put the most interesting pressure on the Beliefs that the player has authored for their PC.)
Again, fictional "reality" is not more "amorphous" in one case then the other. But the relationship between rolls, stakes, framing, consequences etc is quite different.
TL;DR: framing the contrast in terms of "amorphous fiction" is, I think, unhelpful. As
@darkbard said upthread, narrativist play typically produces rich, vibrant, concrete fiction for its participants. The contrast is in the process of play and how decisions-making around framing, stakes, consequences and rolls all fit together. There is no neutrality in narrativist play; on the GM side, no attempt to simply present a situation and perform roll-guided causally-constrained extrapolations from it. That's the difference.