Let's look at a murder mystery I ran quite a few years ago.
The PCs were approached to uncover the murderer of a beautiful foreign noblewoman the PCs had previously met.
In reality, she was murdered by her evil younger sister for court intrigue / personal romance reasons. The younger sister had used a couple of simple illusions to cast blame towards a royal son known to be a womaniser.
There were clues readily available to find the real killer, not to mention the PCs were of a level that magical divination was a real possibility. I expected the PCs to pierce the fabrication and find the culprit.
Instead, the PCs bought the overt story, investigated only to verify their prejudices were correct, and discarded any evidence that contradicted their premise. They presented their finding to the court and the royal son was banished from the kingdom and became a new threat to the group. The evil ilusionist consolidated her power in court and became more dangerous as well.
Why is that story inferior to the original expected ending of piercing the fabrication and finding the bad guy? Why should a GM push a particular set of choices and/or specifically override a random result he decided to roll in the first place?
Actually, I have no problem with that outcome. So revise whatever I said to include the mental agility to allow for that.
I think part of the communication problem is in trying to rapidly codify how I do things, which is much more complex than making generic statements.
For instance, when I use "expected outtcome", it doesn't mean I force things to that (though it doesn't mean a GM couldn't). It simply means that when i present an opportunity to the player, there is a default expected path I think they will take, and a default expected outcome.
If the quest is "catch the killer", I write material that I think will support that, including the capture of the killer. I then go back (if I have time), and identify any "weak" spots where I think a deviation is more likely for the players (meaning I made a huge assumption about how they would approach something). I then put some more material or notes on "if they don't pursue X, show them something else"
I do it this way, because it is less work than trying to build some kind of mega-flowchart of the game choices and possibly outcomes. Since I'm not building some very location-based (where all I really need to do is describe who and what is at each room), this method works OK for me.
I can't say what PC does, but mentally I liken it to a similar concept. I like to have enough material so I know who the PCs may fight or interact with, and the places these things may happen, and a rough outline of the basic "defaullt" chain of events. After that I wing it. I suspect PC wings it more than I do. But we both seem to try to run light on written content (I use maybe 3-4 pages of material).
I have run campaigns where the dice (except for secret rolls) were done in the open. There are times where it is harder to lighten up on the PCs when I do so. In effect, it makes me feel more adversarial.
To return to what Nagol said, if I put in fake clues like that, then I already see 2 default outcomes. part of the point (to me), of playing with players, is when I create the situation like Nagol describes, I want to see what THEY make of it. And I'm much more interested in the social outcome of it, than any combat outcome.
If my players are actively pursuing the goal, I cut them some slack and try to make sure their choices ultimately pan out. if they picked Left (with no evidence that it was better than Right), I'll make Left eventually get to the castle or bad guy or whatever. it's really a matter of what choices they make really matter, and what choices don't.
For instance, where I went to lunch today has less bearing on my life and "what happens next" than the time I spent on this thread, instead of writing code. "choice" versus "Choice"
