Even if the rules and procedures sanction the GM to declare a new fact which establishes that the Countess was the killer rather than the Earl, the fact that it was not established until that fact was declared means the players couldn't be reasoning toward that conclusion--as, very literally, there was nothing to reason toward until that declaration occurred. This isn't fudging, but it does break the chain of player reasoning; everything they have previously observed remains in a superpositional limbo between "valid clue pointing to the real result" and "false lead trying to prevent you from finding the real result", and both results are perfectly consistent with the fiction of a whodunnit situation. When both results are perfectly consistent with the fiction but mutually exclusive and (usually) jointly exhaustive, it becomes impossible to do any reasoning with them.
I don't like thinking about this stuff but my mind does its own thing and so I ended up jotting down the skeleton of two games to work through it. Some brief thoughts at the bottom.
THE 'REAL' KEY
The occult apocalypse machine is ticking down. In one hour the world will be devoured. You need to find Albrecht Wainwright's key to stop this. The key lies somewhere in his study.
GM: Think about Albrecht Wainwright a bit. He's an occultist of some sort. Maybe a medical genius, maybe someone who spent too long thinking about the metaphysics of maths...
The location of the key: The key is somewhere in Albrecht's study. Think about the precise location. Base it on the personality of Albrecht. Maybe if he's a medical occultist it's located within a skull on a shelf. That type of thing.
PLAY
The players ask questions about what's here and the GM can give rough details. If the players ask more probing questions then the GM gives even more details.
The GM marks time when things are studied. Half a minute at the minimum but as long as the GM thinks it will take (tell the player how long you think it will take before they engage in study)
The players can also smash things, open them, burn them, that kind of thing. Tell them the time it will take and mark the time
GM MAKES STUFF UP
Your job is simply to say what Albrecht would have in his study and mark time. Some of the stuff that Albrecht has may provide possible clues as the location of the key. That's none of your business though. Your job is just to say what Albrecht has in his office.
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ALBRECHT'S METAPHYSICAL MYSTERY KEY
Make up Albrecht but not the location of his key. Play the game as above but when the player investigates something, decide if Albrecht would have put his key there.
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THOUGHTS
If 'reason' means heuristic/strategy, then there probably are better or worse strategies in both games. Although I suspect the strategies will be different. If you add a few more rules about how you either convey information or ask for information, the strategies will probably diverge even more.
In the state the rules are in. I'm not sure they're that good but I'm guessing a lot of GM's who play this sort of stuff have a load of 'hidden rules' that they're using without even necessarily being aware of them.
@EzekialRaiden I think one can evaluate the rules, both hidden and written down, by how well it produces that flash of learning/insight you were talking about earlier. That's the social/aesthetic reward toward which games either contribute or don't. Although that's also got to be off-set by 'play feel'. You're not just looking for flashes of learning, you're looking for those flashes in a game that's similar to the ones above. I'd actually bite the bullet and just say that the players are trying to discover what's in the GM's notes. It's reductive and strips away the magic but it's by stripping away the magic we can evaluate the raw mechanisms by which something operates. (mostly fiat but as we've established, fiat is itself a stripping away, not all fiat is the same)