It seems like a lot of people don't approach the game that way, and I wonder why. Assuming that's true, is there a flaw in the text somewhere, or is it something else?
I think your conjecture is true (at least on the basis of the posts I've read on these boards over the past few years).
The relevant components of the text are, in my view, crystal clear as far as they go:
PHB pp 179, 259
Whatever the details of a skill challenge, the basic structure of a skill challenge is straightforward. Your goal is to accumulate a specific number of victories (usually in the form of successful skill checks) before you get too many defeats (failed checks). It’s up to you to think of ways you can use your skills to meet the challenges you face. . .
Your DM sets the stage for a skill challenge by describing the obstacle you face and giving you some idea of the options you have in the encounter. Then you describe your actions and make checks until you either successfully complete the challenge or fail.
DMG p 74
Begin by describing the situation and defining the challenge. . . You describe the environment, listen to the players’ responses, let them make their skill checks, and narrate the results. . .
Sometimes, a player tells you, “I want to make a Diplomacy check to convince the duke that helping us is in his best interest.” That’s great—the player has told you what she’s doing and what skill she’s using to do it. Other times, a player will say, “I want to make a Diplomacy check.” In such a case, prompt the player to give more information about how the character is using that skill. Sometimes, characters do the opposite: “I want to scare the duke into helping us.” It’s up to you, then, to decide which skill the character is using and call for the appropriate check.
DMG pp 73, 75
When a player’s turn comes up in a skill challenge, let that player’s character use any skill the player wants. As long as the player or you can come up with a way to let this secondary skill play a part in the challenge, go for it. . .
Always keep in mind that players can and will come up with ways to use skills you do not expect. Stay on your toes, and let whatever improvised skill uses they come up with guide the rewards and penalties you apply afterward. . .
In skill challenges, players will come up with uses for skills that you didn’t expect to play a role. Try not to say no. . .
However, it’s particularly important to make sure these checks are grounded in actions that make sense in the adventure and the situation. If a player asks, “Can I use Diplomacy?” you should ask what exactly the character might be doing to help the party survive in the uninhabited sandy wastes by using that skill. Don’t say no too often, but don’t say yes if it doesn’t make sense in the context of the challenge.
Taken in isolation, this rules text makes the procedure clear: the GM frames the situation, which will include some signals about options for the PCs; the player declares an action for his/her PC, which (perhaps with the GM's help, and some back and forth negotiation between player and GM) is expressed as a skill check; the check is made and success or failure adjudicated and the consequences narrated; the re-framed situation is then explained by the GM; rinse and repeat.
But look at how the rules are located in the books - to get the relevant rules from the DMG, for example, I have to go back and forth over multiple paragraphs on multiple pages, with duplication but no single coherent statement of the procedure.
And there are other featurs of the rulebooks that push in other directions - in particular, the rules for single skill checks in the PHB, and the lack of any discussion of how single checks (and even sequences of single checks, such as might happen in a combat with many pits to be jumped over) are different in resolution from a skill challenge.
Furthermore, there is no discussion of the sorts of framing and narration techniques a GM needs to make a skill challenge work. The comparison to Burning Wheel and HeroQuest revised in this respect is particularly telling: HQ rev, for example, expressly discusses narrating details into the situation in order to support the (metagame determined) difficulty levels; and BW discusses how to narrate failed skill checks by reference to failure of intent rather than failure at task.
Finally, there is the actual format used to present skill challenge encounters. The only way to make any sense of this, in light of the actual rules, is as analogous to a combat encounter with suggested tactics. Every GM who is not a rank beginner understands that the suggested tactics for a combat encounter can change in various way - for example, the PCs might enter from a different route, or under cover of darkness, or having lured one of the NPCs out of the room first, etc. But many 4e players seem not to have understood the skill challenge format, with suggested skills and actions, as comparable to that: a guide to the GM to help adjudicate a skill challenge if the players take the most forseeable path, rather than a pre-determination of how the encounter
must unfold. And the format itslelf singularly fails to make this clear.
A striking contrast is the formatting in the original HeroWars Narrator's Guide of the extended contests in the example scenarios. These are, for present purposes, just like skill challenges. But the text and layout makes it clear that the lists of abilities and actions are suggestions to the GM for adjudicating likely player choices, and for helping the GM flag to the players what their options might be. No one would look at the encounters in those sample scenarios and interpret them the way some people have interpreted 4e skill challenges.
I think it's bizarre that WotC, in presenting a mechanic so obviously derivative of games like HeroWars/Quest, Maelstrom Storytelling, Burning Wheel etc didn't try at all to emulate some of what is successful in the rulebooks for those games, in conveying how mechanics are meant to work, and in presenting extended contests for pre-packaged scenarios in a way that makes it clear that it is not a predetermined mechanical recipe that the players and GM are just expected to follow robotically.
I did my best in my hack to make this impossible. I tried to make it so that, without engaging the narrative, you could not proceed with resolution. You would not have enough information to set DCs or modifiers to the d20 roll.)
That makes me think of some things I've read Vincent Baker say about Dogs in the Vineyard.
I don't think my adjudication and approach is as toothy as that: for example, DCs can be set without engaging the narrative, by reference to the relevant chart.
I do my best to get toothiness at the point of adjudication - if it's not clear what exactly the PC is doing, or trying to do, I can't narrate and reframe the scene in response to the character's action - and so I work out with the player what exactly is being attempted, and hence what exactly is happening. Generally this happens before the dice are rolled, because my general practice as GM is to restate back to the table what is being attempted with a skill before the check is actually made. (I think this might be a habit more common in traditionalist GM?)
I think the difference is that, when I have the specific details of the situation - map keys and who is where doing what - then I'll use individual rolls. When I have an abstract situation - I don't have a map, I don't know where the NPCs are or what they're doing - then I'll use a skill challenge. In the abstract I think it's easier to maintain player agency with a skill challenge, but if you have concrete details then I think a skill challenge can harm player agency.
This is an interesting hypothesis that I don't think I've really tested.
I tend to play with a very loose sense of the situation - basic ideas about geography, NPCs etc - but tighten thinks up in the course of play and resolution. So most of the time my situations are like the "abstract" one you describe, and skill challenges work well for that.
But suppose I had drawn up a map with a river, a log falllen partway across it, a leaky raft on the other side, etc, and the goal of the situation was for the PCs to get across the river - then I'm not sure a skill challenge would work, because the metagaming that a skill challenge requires (in narrating consequences, introducing and managing complications, etc) seems at odd with the very concerete ingame details of the situation.
Would that be an example of what you have in mind?