It's not like he has notes that say:
the BBEG is running to point B. he is not walking, galloping, prancing, meandering, hopping or skipping. He does not trip over stones because the street is smoothly paved. There are no salesman on this street to sell old documents to, nor are there any sailors who are better than the Dread Pirate Roberts.
Therefore lacking such notes that negate any question asked thus far, the GM has to decide if it exists or not. Which is fine. though saying Yes would probably make things more interesting an reduce RR danger, as the players would be enabled to try somethingg NOT on the DM notes.
Heh, I'm not usually that explicit, but I do, in effect, often have notes that say that kind of things. See, the players that frequent groups that fit my style tend to like both some narrative control and some firm limits to push against. So I'll tend to farm out narrative control in some places, but in others run something a bit more traditional.
And I'm not merely talking narrative control in terms even vaguely related to player agency, but rather the player actually taking control over the story. I have no preference one way or the other whether the captured goblin prisoners will be willing to travel with the party, teaching the party fluent goblin in the process, in return for a negotiated peace on the border. So if a player wants to pursue that storyline, I'll let them. It might not work out (as I'll monitor behavior from the goblins' perspective), but I really don't care. In effect, the player is setting up her own challenge, in a manner that interests her. I'm enthusiastic about
that, even if not the details in this case.
OTOH, I'll have those firm limits. The legendary axe, the "wood wight," is in a particular location. Trying to find it are the party, a rival party, a group of elves, some trolls, and the aforementioned goblins. That's firm on my part. No amount of player narrative is going to short-circuit that process, because that is the challenge for the whole party. Player agency via the character can (and probably will) handle each part of the challenge as it arises. Player agency may manage a "divide and conquer" strategy to make the challenges easier, or something else. But there will be no player narration that escapes or otherwise nullifies the challenge.
I'm not particularly wedded to this odd mix from a game theory angle, but it does seem to work for us. It gives the players that want to truly narrate some room to play, which also takes a lot of the prep work off of me. Meanwhile, since I can focus my prep on those handful of things with firm limits, I do a better job with them. And some of the players feel like this gives the world more nuance, as part of what their characters do is push, and see what pushes back.
So I'm fine with saying yes most of the time. I'm not fine with
making something work, or trying hard to give it a chance to work,
merely because a player asked. That they asked is a sign of interest, but it might be the interest of, "I want to find where the world pushes back." (What I do instead, when a player has a great, flavorful idea, on an aspect that is firm--I make a note, and use that idea as the basis for something else firm in the near future, but unrelated to the current challenge.)
So, in regards to the OP, I could go either way. If I have in my notes that the route chosen by the NPC is the shortest route, then that means that it is the shortest route. If the NPC is reasonably intelligent, and had this planned, then that becomes one of those firm limits. You can chase him on that route, but if you try to go some other way to head him off, it won't work. He outsmarted you here. OTOH, if I have no such plans, then I don't care what happens, as long as they players enjoy him. They can try to head him off, or whatever.