I'm none of these people, but I'm definitely in the other camp, so I'll take a shot.
A question for you:
What does it mean to "solve" an investigation scenario under the light of a pre-established, pre-written mystery backstory?
It's obviously conditional, and starts with the same question: What is the player's goal?
- Are they trying to apprehend a criminal?
- Is this entirely a forensic exercise into something that's already happened?
- Do they need evidence of what's occurred to persuade a third party?
The important thing is that the players want something that can be evaluated. Did they capture the criminal? Did they discover what happened? Can they prove it? The gameplay portion comes in stringing together together actions that can get them from the current state to that end state, and the evaluation at that time. Meaningfully, it needs to be contingent on their choices. You correctly identify that there is really no game if there is no contingency, but I dont' particularly want to deal with the most dysfunctional form of play you present here:
Is it when the players correctly guess the culprit's identity? Is it when they reconstruct the entire sequence of events the GM prepared? What if they miss half of it, but still catch the culprit — is that a solved mystery? Or what if they uncover the full backstory, but only after the GM spoon-feeds it to them through exposition to finish off the session? Is that a “solution”?
It would be easier to have this conversation if you didn't pepper everything you said with this stuff, as if it must be normative. That railroads can exist doesn't mean they must exist, and we should set the case we all agree is degenerate (give or take bloodtide) outside the discussion.
Is it when they take action against the culprit and bring them to justice? What if they do that without understanding the full context. Is that still "solving" the mystery? What if they kill the wrong suspect but uncover the actual backstory later?
Is it when the players themselves understand the backstory, or when their characters do? What if the players piece it together out of character, maybe a week after, but the PCs never quite grasped the full picture? Is that a solved mystery?
What if the players correctly identify the culprit, but the culprit escapes? Is the mystery “solved” at that point? Or does it only count if they both discover the answer and successfully confront or apprehend them?
What if they expose the entire backstory, piece it together beautifully, but the culprit dies offscreen, or flees to another country, or is killed by someone else before they can act (This would be bad play in story now, but maybe acceptable in a more neutral style)? Is that still considered solving the mystery?
What if the players solve the mystery too late. They figure out who did it, but by then, more people have died, more crimes have been committed, and now those events have opened up entirely new mysteries? Is the original mystery still "solved" in any meaningful sense, or has the investigation simply unfolded into a larger, evolving situation that can’t be neatly boxed into whether they cracked the initial case?
I'm lumping the next bit together, because I think it's dealing with an essential misunderstanding; it does not matter what the player's goal is. The whole engaging thing of an RPG is that the "fiction" bit allows players to set unusual and largely unbounded goals for play. They differ from other games that end after 7 turns, or when a player has acquired 100 victory point, or when the stock market crashes in the simulation. Instead, it's the job of players to set their own goals for play. There's usually some negotiation about those goals, the whole trad process of presenting "plot hooks" is essentially just advice about offering up interesting suggestions for those goals to players, and lots of play has traditionally made the acceptable space for what goals a player might pursue very small (get wealthy, kill your rival, save the kingdom, etc.). I think there's a laudable trend toward increasing pre and during game negotiation for what goals are within the scope of play, interesting/agreeable to all participants and the GM will thus be able to prepare for, which is nice, but I don't think a fundamental change.
All of these questions come down to whatever it actually is the players want to achieve; player goals are where the role-playing comes in it is within imagination that any of the situations you propose might be acceptable win or loss states for solving a mystery, depending on what the players have tried to achieve. "Mystery" tends to come down to deduction though; can I put together disparate sources of information to narrow a pattern down to specific outcome? The answer might very well be no, in which case we move back to the basic questions the game poses (are you still alive, do you still have the ability to declare more actions, do you want something else?) and then go from there.
I was writing more on this, but this is moving very quickly, and I wanted to jump ahead to something else that stood out starkly to me.
That’s a valid aesthetic preference. But it’s not the same thing as saying that the existence of that backstory is what makes the mystery “real.” What makes it real is whether the players' engagement with the investigation carries weight in how the fiction unfolds. You can structure that weight around mental struggle against pre-authored material (the puzzle solving element), sure — but as many on the other side have tried to made clear, you can also structure that weight through emergent, procedural play that makes the ongoing and developing mystery have real consequences and provoke hard choices on the go.
I think "aesthetic preference" is doing some real heavy lifting here; this is a matter of gameplay, not set dressing. It is, technically, an aesthetic preference that I'd rather play Big 2 than Go Fish for sure, but the reason is not because the cards look any different, or that an outside observer unfamiliar with either game could even tell the difference at a glance or even with a transcript of play.
The gameplay is different between the two, and in this contrived example, obviously better in the first case. The decisions I will make between the two are texturally different; there are more points of interaction in Big 2, the impact of each decision on the end of the game and on each subsequent decision is bigger, and the impact of my decisions on victory is greater than the initial state of the deck in Big 2 than Go Fish.
"Affecting how the game unfolds" simply isn't the entirety of the goal here. The point is to let players make interesting decisions, and for those decisions to be interesting, there must be a means to evaluate them. The gameplay loop that makes all that possible requires there be a reference state the player's choices can be compared against to see if they got what they wanted. A mystery, the thing the players want involving information that is unknown to them, but theoretically learnable, can lead to those interesting decisions as they try and get it.
Choosing to evaluate play entirely in terms of whether what happens has "real consequences and provokes hard choices" is as much the aesthetic preference on display here. You're picking a presumably appealing fictional state as more essential to play than what I'd call the "quality of gameplay."