I think this both misses some of the nuance and frames it in a way that just doesn't match what the experience. It is like describing a boxing match as two men swinging their arms till one falls down.
A textbook description of eating is not the same as the experience of eating. That's a truism.
@hawkeyefan is not trying to evoke the feeling of being there. He's trying to analyse the process of game play. He's writing as a technician, not a poet.
And in fact his analysis is not like your putative analysis of boxing. Your description of boxing does not include any account of
purpose, or of what follows from that - all sorts of choices about how to stand, how to move, etc.
But to talk about the players declaring actions so as to prompt the GM to reveal elements of their notes
does include the relevant purpose.
It isn't that you are simply prompting the GM to say something. The GM has modeled a crime, who committed it, what evidence they left, etc. There is a mental map of this thing and that model is what people are talking about when they say it is real (and again, to be clear, no one is saying it takes on real world substance; just that the idea of it is concrete and objective). The process of solving it is also real. The players are deducing facts, they are going to locations in the game, discovering clues, putting those clues together. And they can be wrong or right in their deductions.
But the players don't go to locations. They stay in the same location. The players
imagine characters going to locations. And the GM shares that imagination. And this is precisely what determines what bits of their notes the GM is obliged to reveal.
No one denies that the players are reasoning. For instance, the GM tells them "You see blood in the kitchen sink". The players then perform reasoning like
blood is a sign of injury,
blood is a sign of a stabbing,
blood loss causes ill-health,
ill people go to hospitals, etc - and they then make conjectures as to what actions they should declare for their PCs so as to get more information from the GM.
Of course, this can break down - perhaps the GM hasn't thought about the hospital angle, and so has nothing prepared to say, if a player says that their PC goes to the hospital looking for stabbing victims. And I think part of
@hawkeyefan's reason for saying there is no
real mystery is to make this sort of point. In the real world, in a real mystery, there is some fact of the matter about who was where when, about whether or not anyone ever went to a hospital. But in the sort of gameplay we are talking about, the
real facts are facts about what the GM has authored. And these may not cover every inference or conjecture that the players make. In the real world, if I go to a hospital trying to find out about stabbing victims, and someone at the desk gives me the brush-off, then there is a fact of the matter about whether they don't know, don't care, are protecting private information, are part of a conspiracy, etc. But in the game play, if my PC goes to the hospital and the GM has a NPC give me a brush-off, perhaps what is happening is that the GM is trying to get play "back on track". And if the GM hasn't authored anything further, there is no fact of the matter about what the brush-off means
in terms of solving the mystery via play, even though we are all presumably committed to the principle that, in the fiction, the NPC has some or other motivation.
In mystery-solving play, the sort of issue I've just described is somewhat analogous to those parts of the Alarm spell identified in the OP as requiring GM fiat to resolve.