Really?
The players declared that there were guards at the gate? The players declared that the town was there? What, exactly, is the DM reacting to? Yes, the players will react to what the DM puts in front of them, fair enough. DM describes, players react. DM then describes again. Wash, rinse, repeat. That's the basic play loop. At no point is the DM "reacting" to anything. The DM is dictating results. The DM is narrating results. But, at no point is the DM actually reacting to those results.
And any result is 100% determined by the DM. The DM can narrate any result he or she feels like. Now, that narration will generally be constrained by what the table will accept, genre conventions and table social contract, but, beyond that, it's 100% up to the DM. The Dm decides that the guard is unbribable, and that's the truth of the scenario. At no point can the player take any actions or make any declarations that will change that.
I'm getting the sense that many of us are talking past each other because, to me, this is self-evident. There is no objectivity here. The DM is making decisions and narrations that will be fun (hopefully) or interesting (again hopefully) to the table. That's an inherent bias right there. Even the idea of "the world reacts in a logical way" is still absolutely constrained by what the DM thinks is logical. I had a DM absolutely declare that plate mail could not exist in the world because it was too technologically advanced. When I pointed out that plate mail predates chain mail by about a thousand years, I was told I was a bad player for questioning the DM.
Everything the DM does is going to be subjective. That's unavoidable. Sure, the DM can try to be as objective as possible, but, that's not the same as actually BEING objective. Hell, I don't want to play with an actually objective DM. If I did, I'd stick to CRPG's.