Just to reiterate -- I have no idea what's going on in this particular case. I just wanted to note that we don't know both sides of the story here. There's still a lot of room for the story to shift sides without anyone deliberately lying -- two radically different interpretations could be in play.
And I don't think I explained myself well at the end, there. In my opinion, "Railroading" has to involve DM metagaming, not merely NPC action.
Example:
DM: "Now, you must go and slay the Orc King Givrok!" declares the emperor.
PC: Um, no?
DM: The emperor glares at you. "I have been kind and lenient in the past, but if you no longer have any interest in serving me, your usefulness is at an end."
PC: Fine. I'll do it. I leave town, wave, and then head off in another direction completely.
DM: You walk for a few hours, and then a ghostly image of the emperor appears before you. "I see you have decided to take a circuitous route to slay the Orc King," he says. "It may be to your advantage to hurry, as I introduced a poison into your bloodstream that will strike you dead in three days -- a poison that you will find most difficult to eradicate on your own."
Is that railroading? No.
The PCs could:
1) Guess that the emperor is bluffing and keep walking.
2) Dedicate their efforts to getting the poison out of their bloodstream.
3) Demand that the emperor remove the poision beforehand, in exchange for which they will kill the orc king and then leave the empire.
4) Go meet the orc king and see if his shamans can remove the poison.
5) Head back to town and try to kill the emperor.
Is it easy? No. Is it a situation with a clear and happy solution? No. Should the DM always make the situation this way? No. But it's not railroading -- assuming that the emperor is known to have magical poisons, scrying, and image projection abilities at his disposal.
Other Example:
DM: "Now, you must go and slay the Orc King Givrok!" declares the emperor.
PC: Um, no?
DM: You have to. Your alignment is Lawful, so you have to obey him.
PC: I change alignment.
DM: You can't. It's ingrained.
PC: (sigh) I agree to do it. (to friends: Let's just leave town.) I walk out of the room.
DM: The emperor's guards disarm you and hit you with paralyzation spells, and then you're geased.
THAT's railroading. The DM has completely ignored the rules and simply declared that the guards stop the PCs, despite the PCs probably being higher level and more powerful. The PCs got no saves against the paralyzation spells or the geases.
Also, the guards knew to detain the PCs through some sort of NPC telepathy (like someone else's examples above, where thousands of guards just appeared and moved hundreds of feet per round). That's DM metagaming (unless the PCs were being Detect-Thoughts'd), and that's also railroading.
Dunno if others think that's too fine a distinction, but as the DM, I should be allowed to have NPCs make ultimatums. The PCs should always have a choice, though -- even if it's an unattractive one.