The DM decides it. Either by their perrogative via world-building and NPC control or by random chance, their choice.
Would the players have complained if the DM judged the kobold DID know everything and spilled his guts??? NO! They would have been thrilled. Yah! Woo-hoo!!! We captured a kobold and got the info we wanted. Yeah, us!!!
It is only when the DM decided against the players that they felt it was railroading when he provided no useful intel.
Well yes, when the DM blocks player action so that play only goes the way the DM wants rather than the way the players want, that's railroading.
Preferably, there were have been some mechanics involved here. A roll of some sort to interrogate, a Saving Throw by the kobold to resist, or even just a comparison between Hit Dice and Level or similar.
But if the DM is not going to use mechanics... if they're just going to decide the outcome... yes, I think it's preferable that they go with what the players are trying to do instead of block them for some reason.
Not sure how you can't see a difference here.
How is it "crappy"? It is just something that doesn't go the players' way. Unfortunate for the players yes, but nothing wrong with it as a DM.
It's crappy because it's a kobold. The typical kobold is... in my imagination... isn't (a) tough enough to really withstand an interrogation, (b) loyal enough not to try and save its own skin, or (c) stupid enough not to know something useful that the characters are asking about.
It's clearly a case of the DM just not wanting to give the players intel. And to me, that's a crappy DM. I tend to provide an abundance of information, and I kind of expect that when I play, as well. I want to see what players do with the information. I don't want to hoard it and make them work endlessly for a drizzle of info so that the game goes exactly the way I foresee it.
Yes, the DM has. Just like when the PCs get to the door and the DM decides it is locked. The DM shouldn't have to "roll randomly to determine if a door is locked or not". DMs decide how the world operates all the time. It is part of their job as world-builder and storyteller.
NO DM in ANY GAME determines everything by random roll that I know of. And if such a game exists, don't tell me about it, I'm better of not knowing about that crappy of a game. After all, the players don't decide everything their characters do or know by random roll, why should the DM?
I'm not talking about determining
everything with a random roll. I'm talking about involving the mechanics somewhere... anywhere... in the process.
When all the factors of a given situation are decided solely by DM whim, then the DM is controlling the game, not facilitating the game.
Ok, good example! The DM should absolutely NOT just "decide if the interrogation will get the kobold to spill the beans".
The kobold breaking under the pressure of interrogation is the kobold's AC, it's "resistance" to the "interrogation attack".
This could be a static value, a "DC" the players have to get, or could work in the other direction and be a morale check the DM rolls for the kobold against a set morale value.
The kobold knowing information is the kobold's HP. In this case, knowing nothing would mean the kobold has like 1 hp.
So, the DM does get to set the amount, if any, of the information that kobold might know--just like the DM sets the AC for the creature the PC attacks
Sure, if some kind of rules were used to determine the outcome of the interrogation, then I don't think you'd see the complaints about it.
If I try and use Intimidate to interrogate a prisoner, and I roll poorly, I accept that I don't get any information, or that the information I get is nearly useless. That's perfectly fine!
The key difference is the absence of mechanics here. It's not about players just expecting everything to go their way... it's about the fact that a game is being played, and they should have the ability to steer the outcome of the game.
As long as the DM used a mechanic to determine IF the kobold would succumb to the interrogation (morale check, reaction roll, etc.) the interrogation, itself, did not fail. That they learned nothing useful is not the same thing.
In the example, he did not. That's the entire point.
The DM decides what NPCs know or don't know. It is really that simple and not railroading. Now, if the DM didn't use any system to determine IF the kobold would give in?--that would be railroading.
That's all that anyone is saying. So it seems you actually agree?
2) The fight cannot be avoided (it's the encounter!). The DM sets up the scene of the chase and the PCs get to the door but it is locked. Roll initiative.
This is also railroading, no? I mean... "it's the encounter!" is a pretty thin justification for the DM to make something happen.
If the DM introduces a chance to escape from a fight, then I would expect as a player that such a chance may work.
LOL you do you, man.

That is all totally good scene development IMO and very much D&D!
No... eschewing all mechanics in favor of the DM determining all variables is crappy DMing.
What would YOU DO differently, huh? Where in that chain of decisions does the "good DM" do things differently?
- You don't design the layout? Well, I think you probably do unless you roll the city layout randomly?
I'd likely not have every street mapped out, so I'd likely establish these details on the fly.
- No alley? Ok... then where do the PCs go when they encounter the killers? Wherever that is, you just decided that instead of the alley.
I'd present choices that may be relevant to the players and their characters, and provide them details to choose their path.
So let's say the alley was one thing... I'd maybe also provide a gutter that could be used to climb to the rooftops. And perhaps a gathering crowd into which they could try and slip. I'd present the risks of each along with their description. "The door in the alley is likely to be locked in this part of the city... can you pick it before your pursuers reach you?" and "The gutter looks somewhat rickety, but should support your weight. Can each of you climb quickly enough to get up there before the pursuers catch up?" and "The crowd is pretty large, but mostly made up of commoners... simple folk in simple dress. Can you blend in somehow, or will your weapons and armor give you away?"
Something like that. Offer choices, let the players choose. Allow each of these options a chance to succeed.
Otherwise, there's no point in the chase. If you want the fight to happen, just make it happen before the chase. Still seems like railroading to me, but at least it saves some table time and some potential frustration.
- No door? Fine, then the alley is a dead-end and there's going to be a fight. Which is why it's an encounter.
I wouldn't do this. This is railroading.
- Not locked? Fine, then no encounter--the PCs escape. You just narrated the choices for where the PCs can go and they decided where to go. But then the "encounter" was never going to happen unless the PCs just decided they wanted to fight--but given the original synopsis fleeing seemed to be the decision. But then this begs the question: Why THAT door? Where does it go? Didn't you just "railroad" the PCs into going through the door--just like YOU wanted???

No, I wouldn't offer only one choice, and I'd also likely involve mechanics of some sort. There might be a DC to pick the lock or break the door. I may even just make a fortune roll to see if it's even locked to begin with.
Having only one option is a pretty clear indicator of a railroad, no?
- How far the pursuers are? Close enough to begin the encounter, otherwise why bother??? The DM could randomly roll this (I often do), but the range of the roll is still determined by the DM, right? So, close enough to begin the chase, but far enough that it isn't an immediate fight.
I'd set this based on the circumstances, and would let the players know. "You have three rounds until they're on you" or what have you.
So, in other words, it "makes sense" if it makes the players happy and they don't see the outcome as failure?
Seems like railroading to me--just in the players' favor.
That’s because you’re failing to realize that the criticism is about the lack of mechanics, and the difference between blocking player actions and allowing them to succeed and how that impacts player agency.
It’s remarkable, really.