You're addressing the specific example and not the general point. Irregardless of why the DM would/could manipulate the DC's... It is still a limiter on player agency because determining the DC is DM whim. Even if you tell the PC's what the DC is it still is determined (and thus their chance of success) by you. Like I said earlier DW is an example of a game where this is truly mitigated but in 4e that's not the case. In the same way secret backstory can limit the agency of players so can subjective DC's. It doesn't have to be a purposeful manipulation... Unless you are being transparent with how you come to choose your DC's, your players are unaware of the conscious and subconscious biases that lead to choosing one DC vs. another. That is a limiter on agency and is an unknown in the same way that secret backstory is unknown.
Much less than you seem to think. I mean, sure, in 4e as written, a GM could present the characters with impossible 200' jumps (DC effectively based on distance) mazes of hazardous terrain, etc. This is not in accord with the encounter design guidelines, and certainly not in accord with the SC mechanics. There IS 'wiggle room' though, to an extent. 4e is only a marginally Story Now SYSTEM though, and GMs using it as such need to keep that in mind. My own 'hack' of 4e is much more rigid in this regard, you really cannot generate arbitrary DCs in HoML. The most you can do is present a situation as being higher level than the party, and thus high stakes.
I do find this discussion interesting though in terms of helping to point out the significance of this feature of narrativist games.
Wait what? Unless the players can now frame their own adversaries, which I haven't seen an example of so far how is this remotely true? @
pemerton has chosen the adversaries that his players have faced in the "story" as far as I can tell and a red dragon could easily be framed as opposition to numerous goals. This isn't really making any sense. unless you are now saying that nothing is allowed to be created without the players "ok" in Stoiry Now gaming... is that the case?
It is the players story, in large part, the story of their PCs to be precise. So, yeah. I mean, sure, a GM could say to himself "The characters love the village and they set themselves up as its champions, I'll put a Red Dragon in front of them and let them decide which dies, them or the village." but to me that's pretty dirty pool, though I guess it could be OK in a grimdark sort of concept game. Even then, the GM is still not empowered to simply make the thing arbitrarily difficult. If he DOES then the players are owed some arbitrarily large reward for success!
Frankly, a 'Kobiyashi Maru' scenario is not totally out of bounds, but really needs to be done in a way that works and isn't underhanded. The closest I ever got to this was setting a Traveler game on a doomed space station, without telling the players ahead of time what the scenario was. I wanted to evoke the whole experience of coming to a realization that their fate was inexorable. However, it was all new characters, a starting scenario, and I know all those players. The 'truth' was not beat into them with a stick either, the whole thing involved the process of realization and dealing with it. It was still tricky, though it turned out really well. By the time everyone died, the end was somehow fitting.