I think the bigger issue is that players can and often will find a way to "justify" almost any skill in any situation... so then it falls on the GM to determine whether their fiction was "good" enough to allow said skill to work in this situation... which can be a major hassle and lead to arguments or the DM just goes "yeah whatever..." and it does in fact turn into just a series of dice rolls.
Meh. I can't help but say "Welcome to DMing." You listen to the player and if the plan is good, you say yes. If it's not helpful, you say no.
Relating this to my post just above:
In play that strongly emphasises the logic of ingame causation - "process simulation" - and which in most cases defaults to GM adjudication and application of that logic, the approach that bill91 describes applies. This is the approach which the phrase "mother may I" is caricaturing.
I think the 4e approach - with its emphasis on "try not to say no" - is downplaying that style of adjudication, and emphasising genre credibility as the constraint. Hence when (on p 42) we have the ogre being kicked into the brazier, we don't investigate the physics of the situation (cf size mods to Bull Rush in 3E) but rather the genre character of the situation (qv Zorro).
A consequence of the 4e approach is that - as Imaro points out - clever players, who can come up with innovative but genre-fitting ways to use their skills - will "justify" almost anything. Imaro presents that as an issue - and for competivitve, challenge-focused play perhaps it is. But I think for the sort of play 4e is best at it is not an issue or a hassle. There is nothing wrong with genre-clever players mostly getting to have their PCs win. This is (in part, at least) what the game is about. And approached in this spirit there is no reason to think the fiction will "drop out" - because the players' cleverness manifests itself in engaging with the fiction and presenting clever ideas that play on it.
and sometimes the DM is the only one to know what will or will not work.
I think that applying secret backstory known only to the GM in action resolution puts a lot of pressure on "player protagonist" play. For instance, players can come up with clever, genre appropriate stuff yet have no chance of success. It makes ingame causal logic more important than genre and theme, and pushes players towards a different style of play - what, at it's limits, gets caricatured as "pixel bitching".
There is obviously nothing wrong with that playstyle - for instance, classic D&D exploration (say, as described by Gygax and Moldvay) depends on it - but I don't think it is well-suited to resolution by the skill challenge mechanic, because there is (i) no reason to think that the players can resolve the situation in any number of checks, if they aren't engaging the right bit of the gameworld in the right way (as determined by the secret backstory), and (ii) once they engage that bit of the gameworld in the right way then the challenge should be over no matter how many checks have been made or not made.
The example of the Duke who can't be Inimitedated in the 4e DMG comes close to this, but I think it's important that it's not
secret backstory - it's accessible to the players with a successful Insight check. I think this is a problematic example of a skill challenge, particularly as their are no design notes, but it probably falls just on the viable side of the "secret backstory" line for skill challenge play.