IME, it's not so much DCs that are negotiated (at least at tables I have sat at) but people's understanding of the fiction. This is where the negotiation happens. Often, again IME, it's retroactive. Maybe there was a clear miscommunication of the fiction between the GM and the players such that the negative consequences the GM narrates in the fiction feel disconnected from the shared fictional understanding of the players. I don't think that players are often trying to "cheat" here, which is sometimes the accusation. This is to say, some GMs here would be quick to accuse the players of fishing for a do-over, mulligans, or cheating. I think that the more common answer is that the players and GM were not seeing the situation eye-to-eye.
I do see a lot of the process of play as a negotiation. The language of "negotiation" was fairly eye-opening for me because there was a sense that I had that the players and GM were trying to suss out a common ground regarding the fiction and the interaction with the mechanics, including acceptable player action:
- "Is this something that my character would know? Why or why not?"
- "Could I do [X, Y, or Z] action? If so, what would I have to roll? I would have to roll that? Okay. So maybe I do something else, like just swing my sword."
I understand and appreciate that you come from a potentially different culture of play where what I and others are describing is foreign to you. However, I have seen a lot of such discussions in D&D all the time at nearly every table at have sat at since I started gaming at the very tail end of 2e D&D, a few months shy of 3e D&D's launch. So the idea of "negotiation" matches pretty well with my own experiences. It's also possible that if I sat down at a table with you to play, you would see no negotiation transpire but I would.