I think you might be misunderstanding Imaro's question.
Why does the GMA ask "prove it" in the first place? Why do they care if the NPC had the knowledge or not? Is it because Janx says so, or for some other reason you can articulate, beyond your personal preference?
I don't know yet.
There is something fishy about the GM claiming the NPC took the perfect route and that my PC cannot find a shorter route.
This is different than my PC trying to claim his skill-check can change the material the floor is made of.
Perhaps, it is guided by my real-life experience with routing software. On this topic, I personally have more experience with the concepts involved and can discern that it is not a simple matter.
it could be akin to a paramedic player calling BS when the DM uses some medical concept incorrectly and a game outcome hinges on that incorrectness. The paramedic is correct, but the DM's wrongness gets in the way.
There's also the matter of what is a Fact in a fictional universe where most of the details are not defined.
The pit existing in Room 1a, 2 squares north and 1 square east is a fact. It's on the map, and quite clearly meant to be there. Its factiness is both weighty and obvious when you enter the room. There may even be a shortest path from the 2 doors in the room around the pit that is provable and testable by its obviousness on the dungeon map. it is objective.
The NPC taking the "best" route in a city is based on fuzzy logic. The DM didn't really measure it. It is subjective that it is so because the facts of it rely on details that are not established facts.
Perhaps that is the difference. Objective Facts which are inherently provable by looking at the stat block, inventory list, room description, dungeon map.
And Subjective Facts which are things the DM says are true, but aren't really born out by Objective Facts. They are instead based on abstract assumptions of the game world.
If we accept that a Shortcut is a different kind of fact than a Pit in Room 1A, we should ponder from there how it is different from other things.
The NPC killed the mayor. We didn't roll for it, so that's a made-up fact. Obviously the PCs object to it, but they were not there to contest it directly.
The NPC planned his escape route. He probably did. How well he planned it is of course up to debate. And Int 10 NPC does not plan as well as an Int 19 NPC.
I think in all cases, we agree the NPC thinks he has the best route. I of course debate that the NPC may not ACTUALLY have the best route.
And that the DM might be making a mistake by insisting it is so.
Up to date, I have been unable to articulate the precise reason why. I can tell you this. When I object to something, it does usually turn out that there's a good technical reason, even if I don't have an immediate explanation. There's something special about this situation, that as a GM, it bears consideration.
PS. When I wrote "I would advise writing that the NPC takes the most direct route in my notes. And at game time, I would certainly disregard it." that was a dyslexic typo. I meant to say I wount NOT advice writing that down.