Out of curiosity, what if the player's flash of insight was wrong according to the DM's notes, but was both better-supported by the clues thus far and made for a better, more entertaining story?
Specifically, let's say the player suddenly realizes that the Princess is framing the Baron, and explains their character's reasoning to the other players. Upon hearing the reasoning, the DM realizes that the clues they had intended to point towards the Baron point even more strongly towards the framed-by-Princess theory. The other players are excited, and start exclaiming about how awesome the solution to the mystery is.
Would you object to the DM "secretly retconning" the framed-by-Princess theory to be correct in this circumstance?
That's...pretty unlikely, but theoretically possible. As I said, I'm not a genius, my players
are collectively much smarter than I am. I would have to very,
very carefully consider how to proceed. I consider it an
extreme risk to do this ever, for any reason, even if that reason
seems really, really good.
The reason I hate doing anything like this is that it makes the world unreliable. The world not only can, but
will change every single time the DM thinks it's a good idea, at which point things like truth and consequences cease to have meaning. Consequences evaporate because the consequences are only what I secretly permit them to be. Truth evaporates because there are no facts--there are only provisional appearances that I, as DM, can secretly overwrite whenever and wherever I feel like.
Another way of putting this is: If you're in a relationship (be it romantic, platonic, economic, whatever) and the other person misrepresents their actions, actively prevents you from trying to find out about it, and if/when called out tells you that "it's for your own good" or "it's in your best interest,"
you should get out of there immediately. That's an incredibly dangerous thing in any relationship that affects your real life. I consider "the game group" another relationship that affects my real life.
But--contrary to what some have said--I am open to considering that I made a mistake, or that I thought I had presented clues that indicated one person was the perpetrator and another innocent when they made far more sense the other way around. If, again in this highly unlikely scenario, I actually did feel I had made a real bonehead maneuver and bungled the clues
that badly, I would not simply go ahead with the players' theory as though that had been the truth all along. I would build
new justifications for why that theory would indeed need to be true.
Part of the problem with this is that, while I can imagine any single clue ending up pointing "the wrong way," I would
never furnish just a single opportunity for such clues. In the actual murder mystery I ran (where an actual Baron was indeed framed for murder!), there were six entirely distinct clues that hinted at the true culprit: witness testimony from the servants and party guests, the time of death (many hours
before the last time the victim was seen), the actual cause of death (poison, not the dagger found in his back, which had been put there well after death, meaning minimal blood on his clothes--clear sign of a fake wound), the actual location of death (his room, not the upper chamber where the body was found), the people the victim had spent time with prior, and forged paperwork traceable to the real culprit if the party read through it carefully, which they did.
So if I screwed up
so badly that I managed to make not one clue, not two clues, but more than half of the clues "point the wrong way"? Well, I've screwed up badly enough that I
need to make amends. One possible path would be to have a trusted NPC provide a hint that specific clues (that is, the ones "pointing the right way," but against the players' superior explanation) are fake or untrustworthy in a way they hadn't been able to detect, so that the players know they need to dig deeper and find the "real" clues (which, in this case, will support their superior theory). Another could be that they discover the "real" killer (that is, the one their superior theory identifies as the killer), or an agent of that person, manipulating the evidence or in some other way tampering with things, again so they can clearly know that the evidence they had is at least partially untrustworthy.
As a result...no, I don't think I would use "secret retconning," because I would draw attention to the idea that some of the evidence they have is fake. I would not, necessarily,
tell them that this was retconning other than after the mystery is resolved. I tend to be very open with my players about mistakes I make, so that I can get feedback and do better, I just sometimes wait until the "postmortem" as it were to lay my cards on the table. But either way, I would make damned sure that the players get a clear signal that some of the evidence that they
thought was reliable wasn't, so they would
know to ask more questions and dig deeper.
(For reference, from my standpoint my notes are just suggestions until established in play or in the player-facing campaign documentation, so no "retconning" would be required to proceed with the framed-by-Princess scenario. But I'm using your terminology since I know we differ on that point.)
This is fair, and in some ways, my notes are similar. However, I have a much more stringent standard of "established in play" than you do, I think. That is, as soon as the clues are even brought to the party's attention, they're locked in. They exist in the world as objects (or states or whatever: see "knife wound didn't bleed, clearly a fake cause of death"), and the instant those objects are perceptible to the players,
even if the players don't notice or mess up investigating them, they're established. I can't change established things without establishing something new. That establishing-something-new
cannot be secret; it must be
at least in principle observable by the party.
I take great pains to stress this for a reason (people have tried to use it as a weakness of my position before): I do not expect the party to
succeed at discovering the true state of things, they can quite easily fail both because the dice betray them, and because they simply ask the wrong questions or look in the wrong places. I am not responsible for ensuring that my players
successfully determine the true state of things. I am only responsible for ensuring
that they can possibly determine it, whatever it may be.
As another example: monster statistics. As long as the party has not actually made an observation of the relevant characteristic, those characteristics remain unknowable to them
even in principle, and thus can be changed. For example, an owlbear. They don't know precisely how hard it is to hit (AC), how hard it is to take down (HP), or how nasty its attacks are (damage) unless they acquire good evidence thereof. Once a combat starts, however? I can't change those things anymore. They exist, they are
in principle knowable, even if the party never actually learns them (e.g. if the beast runs away before they kill it, they won't
actually learn how much HP it had, but they
could have, which means it's off-limits for changing
unless I give explicit opportunity to find out
why it changed.)