But I've seen it called railroading and I've seen it called not railroading.
I've seen it used a bunch of different ways, so to me you insisting one definition is the correct one, simply because you feel it is, as you say- is a stretch.
In fact, when I was more actively going to conventions and gaming at hobby stores (and therefore interacting with a wide variety of gamers) I more commonly saw it being used in the method I mentioned earlier.
Here's the transformation I've, personally, seen over the past 5-6 years. It's grown, I think, because of the re-emergence of Sandbox play and a very active OSR movement - but this is not to say that everyone who sandboxes, and everyone who's into the OSR is responsible. I think it's just an unfortunate example of definition drift.
Before: Railroading is bad gaming. It's a degenerate state of affairs where a DM basically plans both the adventure and the PCs' reactions to it ahead of time. Most problems only have one solution, and there's only one right path - and deviation from that path is severely punished. Stuff like mandatory capture scenes, unavoidable ambushes, NPCs you can't attack, and so on are hallmarks. Railroads are best defined by their inflexibility during play, the lack of player agency over their characters' actions, and the arbitrariness of the DM's decisions. It's to be dreaded as a player, and avoided as a DM.
After: "Railroading" can include anything from linear adventure structures (where the PCs actions still aren't constrained by fiat), to branching flowchart adventures, to even presenting an adventure plot to your group up-front rather than having them pick one from a list of rumors. Opinions vary; it depends who you talk to. "Railroading" gets conflated with other gaming styles, and it's no longer limited to the earlier definitions. However, there's often a caveat - some railroading is
good! Really! It's not all bad, it's just a different way of gaming, so it's okay if you like to be railroaded in your "story-games"!
Personally, I find the latter definition (or lack of definition, frankly) rather useless because nobody can quite agree on it anymore - and the former, negative definition no longer has a name of its own. I also think "It's okay if you like to be railroaded" is more than a bit condescending; the term has historical negative connotations, and pretending they don't exist anymore is a dodge, at best. I think it's more often used in a "my-sandbox-gaming-is-better-than-your-story-gaming" manner. And, frankly, I dislike that this redefinition has been allowed to happen without a fight.
-O