No. In the absence of other instruction from the players, it's just a matter of adjudication. There were many possible outcomes; the DM picked one.
Fuzzy propositions by the player don't automatically give the DM the right to adjudicate the PC's actions as being congruent to the outcome he considers most interesting, and even if they did, the DM is not required to make that his primary concern.
1) The DM can refuse to rule on a fuzzy proposition until the player clarifies what exactly he means. "Do you go bear left, right, or go over the hill?" or "I can't figure out where you are going to go based on generally north. Pick an exact compass heading."
2) The DM can use the simplest and least vague meaning of the proposition, turning "generally north" into "due north".
3) The DM can determine exact bearing by either random selection (picking one of six hexes that are 'generally north' randomly to set the bearing) or by making the bearing 0 degrees plus or minus 9 degrees.
4) The DM can create some sort of random or skill informed walk plotting the PC's travels. For example, if on a hex map, the DM determines which hex is entered next by selecting from the hexes that are "north" of the current hex. In general, I tend to use this method, with a successful navigation check indicating you keep your desired heading and otherwise you drift into a neighboring hex and walk a bendy path. As a result, the players would very much have gone "generally" north, but at no time was I choosing for them their destination based on a desired plot (the pun intended).
5) The DM can pick where wants the players to end up based on what he thinks will be good for the game. This process of play is called "railroading".
It's a total copout to call it "just a matter of adjudication" as if railroading wasn't always a form of adjudication and railroading was the only possible process of adjudication and as if the GM had no option but to choose that one process of play that was railroading.
Fundamentally, we are arguing over the meaning of words. You are insisting that railroading because of its negative connotations is something negative, and therefore, if it isn't a negative then the thing is exempted from being railroading even if you agree that the exact same technique that is used in railroading is being used in this case. But this means you want the definition of "railroading" to be a value judgment, and inherently subjective, and I much prefer an actual objective definition. You are "railroading" when you use the techniques that are used to railroad. No exceptions, nor are exceptions required.
Fundamentally, where you've gone wrong is that your definition requires you to be the objective authority on when a technique is acceptable to use. If you used your technique, and were caught doing it, a player might accuse you of "railroading" them to Mount Fire. You would say, "Oh no I did not. You are wrong. I used a technique strongly associated with railroading, but I did it with the best of intentions because I thought it would be best for the game if you went to Mount Fire. You don't have to go into to Mount Fire, therefore it isn't railroading."
I would say, "Yep. You caught me. I absolutely did railroad you to Mount Fire because I didn't want you to be bored randomly wandering an empty wilderness and I didn't have enough content prepared to make a whole session of visiting those otherwise empty hexes interesting. Now you can get off the rail though, and if you'd rather I didn't put you on rails like that I won't do it again. Just understand that sometimes when you wander off the prepared portions of the map, what I improvise won't necessarily be as cool, intricate or well thought out as what I can prepare between sessions."
Beyond how the two of us would be thinking about this and the mental state we have, for all the verbiage we are quibbling over something very small. As a practical matter, the sorts of techniques that we think are justifiable don't differ at all or very much. It's how we prefer to label these techniques that differs. I'm saying, "All of these techniques are [objectively] railroading, but sometimes they are [subjectively] justifiable anyway." You are saying, "When these techniques are [subjectively] justifiable, they aren't [objectively] railroading." I think your formulation is a bit of nonsense, but as a practical matter the impact on what we'd advocate as good GMing practice isn't changing much.
Beyond the normal things that keep people thinking one way or the other, I've been trying to think why you consider your definition useful. The only thing I can think of is that it allows you to state something like, "Don't railroad." as a categorical absolute rule, something that can't be said under my definition. However, I don't think you can actually objectively explain what railroading is under your definition, making it just something "you know when you see it" and thus the categorical imperative would be meaningless as advice. As you yourself said, the definition of "sufficient" and "meaningful" agency is open to debate.
May I suggest that you might want to think about what else you haven't yet considered.
All the time. All the time. Indeed, I think much of the point of my definition is precisely that it gives you a better vantage point for thinking about what else you might not have considered.
And I did consider it; "fuzzy points of the compass" is definitely railroading. Right now I'm just trying to decide if it is a subcategory of "Schrondinger's Map" or deserves its own category. And one thing that did come out of this. I'm starting to feel I'm getting close to the Socratic definition of railroading.
But don't leave me hanging. What else do you think I haven't considered?
