Bedrockgames
I post in the voice of Christopher Walken
Rustic Hospitality means shelter, and hiding, and shielding, unless there is a threat to the NPCs. So it obliges the GM to decide when such a threat occurs. I strongly assert that it is possible to do this better or worse, and that the better and the worse can be judged by coherent principles that are implicit in the idea of the players as equal participants in relation to the shared fiction of the game. The GM can think along these lines even in a system, like 5e D&D, that gives the GM a very high degree of authority over the shared fiction. (To this modest extent, at least, I agree with @Bedrockgames.)
The reason I considered the rustic hospitality example railroading (though I probably wouldn't say Mother May I, as it has little to with that problem in my opinion, since it seemed to skip over even the players trying to do something), is two-fold. The primary reason is the GM clearly had a story they wanted to tell, and that sort was going to happen regardless of what the PCs did. They said they hid in a barn, there was no apparent reason that didn't work, and it went right to the dramatic moment the GM had envisioned. I'm fine with GMs having those kinds of dramatic moments if they want (it isn't my style but I see nothing wrong with it) but it becomes a railroad if it is going to happen regardless of what the PCs do, or if the deck is weighted so it might as well be a foregone conclusion. In this example, I would have been fine with it if more had been done to make it less of a foregone conclusion. This doesn't even have to involve rolling dice. But some deeper interaction with what was going on so the players could make choices that lead to different outcomes would have made it okay in my book. The other issue is, and I might be missing details that weren't given in the example, the GM seemed to just gloss over specifics and elapse time in a really weird way. Like I get elapsing time when it is uncontested. But if the players are in a dungeon and walking down the hall and you just declare "Oakridge the Filthy confronted you, did an amazing spinning hook kick that knocked all of your heads off, so you wake up in his Laboratory, bodiless in fluid filled bottles." That is shifting the present moment to the past tense in a way that railroads a hook or a dramatic part of the story. And this isn't far off from published railroad hooks I've seen.
There is a Ravenloft Adventure (it might be From the Shadows but it could have been Roots of Evil or a similar module) where, in order for the adventure to happen, the players have to have their heads cut off by the headless rider so they can wake up in Azalin's lab (that is what I based my example on). I don't have the module on me at the moment, but my memory is there was little the players could do to avert the beheading. If my memory is correct that is a railroad in the same sense as the rustic example.
Now I would be totally fine if instead the GM had concocted a contingency scenario where "if Oakridge the filthy happens to take their heads in any fight in the coming weeks, he plans to experiment on their heads in jars in his lab". Or int he rustic example, if the GM had a contingency awaiting should the players legitimately be found and captured. It is the forcing of the outcome that makes it a railroad