I guess I'm drawing a distinction between "just in time prep" and true "no myth" play. With "just in time prep" you say, "They're heading to the Old Sawmill. I'll put 12 orcs there and they can find a clue implicating Lord Turshill." (You could use "just in time prep" to create non-linear structures, of course.)
I like your term "just in time prep" (JITP) to describe the "making it up" that happens in game.
In your example, JITP is defining new game content (a new location, new monsters, and a new clue).
Celebrim's reference to Shrodinger's Trap (or any of his products), refers to JITP activity that creates an entity because the player mentioned it (probably by looking for it). Particularly such that the GM would have forgot to consider if the entity could even be present.
JITP work to create game content to cover a space that was unforseen to be needed, is different than projecting reactions, new activities, and whereabouts of NPCs. Its still subject to Shrodinger, in that if the PCs say "let's check the bar to see if Bob's been there", then the GM may think to put Bob there, so he can move the action along.
I'd like clarification on this "Linear" term.
The PCs go to the saw mill. They find 12 orcs, kill them, and find a clue leading to the Lord. How is this linear (pre-initiative?)
Is it linear because it was written in the adventure notes?
Is it linear if the PCs spontaneously decided to check the mill and I JITP the encounter?
Is it linear because I left a clue to entice the PCs to move towards my expected "final" encounter with the BBEG?
Is it linear because there is a probable outcome (orcs defeated, clue found, PCs follow the clue?
Is it linear because I shuffled some stuff around to entice them toward the BBEG?
I'm not keen on the linear term, as when the encounter itself doesn't seem linear.
Sure, I suspect they'll beat the 12 orcs and find the clue. But technically, they could parley, retreat, sneak and avoid, or even be defeated.
I'm all for content re-use/re-arrangement. I'm not for thwarting of player intent. If the PCs don't want to mess with the Lord, then I shouldn't shuffle content so they still face him.
If the PCs are trying to get to the Lord (presumably involving figuring out the BBEG is the Lord, then going to him), then shuffling some game elements to enable their quest to go forward is acceptable.
Part of that license to rearrange is to get the PCs moving when they fritter their own time (dickering around about hat shopping, instead of finding the man who shot their pa). Or when they mis-interpret a clue, and get in the weeds, to bring in news that turns them around, or to make their dead end actually be the right direction.
In a "if it ain't written thusly, it ain't so" style, I gather that if the PCs go hat shopping, then they waste 4 hours of game time hat shopping unless a random encounter check turns up something. If they keep digging into a dead end of a corridor, then they keep wasting time. If they pursue the wrong suspect, they do that until they stop, and they never solve the mystery.
Just as Shaman assuming that I literally don't put water in the game because the char sheets doesn't say they can swim is taking a concept to a ridiculous extreme, I should hope a sandbox DM exercises some judgement and does something in or out of the game to correct a player stall, even those his notes don't cover it.