I think the reason this isn't landing is because "no one knows if the guard would show up on success or failure" isn't any better, from my perspective, than "the guard will show up on failure and not on success". The guard's appearance is still being adjudicated as a result of an independent action roll.
I don't know what you mean by an "independent action roll".
At the table, the GM's decision is not independent of the roll - it is the result of the roll that requires it to be made. And in the fiction, the guard harassing the character is not independent of the action the character is performing - his singing has attracted the guard.
Yes, we do. The guard is there--that is fixed.
At a point in time - probably around about the time the player has their PC wander the streets of the town at night, singing - you (as GM) decide that a guard is there. Prior to that, the guard is not "fixed", having not been thought of beyond the generic idea that towns have guards.
At a point in time - when deciding how to narrate the failed Sing test made by a character wandering the streets of the town at night - the Burning Wheel GM decides that a guard is there. Prior to that, the guard is not fixed, having not been thought of beyond the generic idea that towns have guards.
The guard is equally "fixed", from the moment of mental conception, in both games. You are talking about a difference of process in the GM making the decision, not a different degree of fixed-ness.
Does 'no one' include the GM?
The GM can't decide what scene they might frame next, before this one has resolved. Suppose the roll to Sing had succeeded, and so Aedhros has gained a degree of self-resolve. What action might I have declared next? Maybe I would have gone back to Thoth to try and talk him out of his mad plans to raise the dead.
Would the GM have mentioned the guard? I don't know - there are a lot of people a character sees when walking through a town that the GM doesn't mention. Would the GM have decided that a guard approaches Aedhros? I don't know, and I very much doubt that the GM knows. I mean, until I declare an action for Aedhros, or we otherwise talk about what we want to do next, how could he?