The GM may not be the author of the end of the story, but, his fingerprints are certainly all over the manuscript.
The GM sets up a scenerio on a certain time frame - a completely linear plot line unless the PC's can time travel - but that doesn't make it a railroad.
See, the problem I'm seeing here is people are contrasting the idea of sandbox with railroad. That's a false comparison. The opposite of sandbox is linear, not railroad. You can railroad just as easily in a sandbox as in a linear campaign.
Do X or bad things will happen to your character might not be forcing the players to act in a certain way, but, it's certainly pushing them in that direction. To me, there's no difference between "You can choose not to do X, but if you do, this shopping list of bad things will happen" and "Just do it".
Because, IMO, at the end of the day, the players will do it because it's pretty obvious that's what the GM wants you to do.
To me, saying, "Well, you don't HAVE to do X, but, if you don't, you get punished" is railroading. Find the Disks of Mishakal or the invading dragon armies will simply come in larger and larger waves until you die may be totally justifiable from an in game perspective, but, it's totally a railroad.
My mileage varies.
I've had player groups decide to deal with the known threat head-on, finesse around it, flee, hunker down to survive then pick up the pieces and start putting them back together, help it Quisling style, and pretty much every combination of those tactics put together.
Additionally, who says the threat needs a linear solution? There's often a wide range of ways for the PCs to approach the problem.
Invading orc army? Defeat them in battle! or Kill the leader! or Poison the food supply! or Convince the Elvish King to help! or Flee to the next kingdom with a warning! or Stage a prophetic omen to convince them to retire! or Bulid up a rival in exchange for peace! or pretty much any other tactic the PCs want to try.