Okay this may be a point worth talking about. I think investigative adventures, are a different animal than a simlulationist or sandbox or living world scenario. There is going to be some extrapolation in a murder mystery. But I tend to think of mysteries as much more structured and concrete scenarios than I would typically have in a standard sandbox (they might come up from time to time, but when they do it is hard for me to not feel like I am shifting into a slightly different mode of play). Just as an example if you are doing a mystery you are going to be mapping out things like crime scenes, clue maps, etc. That isn't normally the type of prep I do in a sandbox campaign. And I get simulation does not equal sandbox, but I mention this because I see investigations as their own beast from the kinds of adventures I often talk about in this discussion.
I think the approach to mystery scenarios you've described is very similar to a simulationist approach to play. There is the information determined ahead of time, and that forms the basis of play, with the GM using all of that to scaffold play and to build upon as needed.
Now, I think almost all RPGs have some amount of predetermination going on which is used as a basis to build upon, but with a simulationist approach... and with the mystery approach you're describing... there is much more determined ahead of time, and it is generally treated as inviolate. This last part is key, I think, and it's what
@innerdude expressed frustration about in his post.
I think that, similar to what I would say about simulationism, what we're discussing is a process that relies on the illusion of cause and effect. What I would say is that for some, the illusion of cause and effect is likely stronger with a GM determining things ahead of time, since that's similar to how the world works. But it's just their sense of things... their opinion or preference.
I think this would depend on what extrapolations you are making. If you aren't changing the core details (i.e. the clue envelope isn't this amorphous thing that can change) then sure. But if you are shuffling those kinds of details around either behind the scenes or through other procedures, I think that does create a different experience where it is starting to feel less like the players are actually solving the mystery and more like they are doing something else. It is like the difference between systems that force you to engage with the setting and be Sherlock Holmes, versus ones that allow you to simuluate Sherlock Holmes effectively through things like Skill rolls (i.e. the player making the deduction versus the roll making the deduction). Both of those are entirely viable but I am using the kind of language I am in order to mark a distinction. Arguably the latter does a better job of capturing a Sherlock Holmes story and of portraying Sherlock Holmes, while the former merely allows the player to experience the fun of solving things like Holmes does if they can. And this example isn't a difference between the different types of games. This can both be done in 'trad' and it just boils down to what kind of skill system, if any, it uses
This is part of the struggle with communication here. There is no "changing" of details in The Between or similar games where the mysteries are not predetermined. It's not a case that something is one way and then it's another. (Or if it is, it's a case of some revelation granting new context to something, which can also happen in the predetermined scenario). The details aren't mutable or amorphous. They're simply not yet known. Once they are established, they are then set. From the player side, there is no real difference. It's only from the GM side that this functions differently.