So let me get this straight... you're claiming that a success/failure can be focused on a particular task... but the adjudicated outcome can have nothing whatsoever to do with the task at hand but instead be based on the overall skill challenge.
Mostly (though "nothing at all" is too strong). If you read the example skill challenge in the Essentials book, that is how it works when the 3rd failure occurs.
And here is an example from p 77 of the DMG:
Jarret: I’m going to try to handle this with diplomacy. My good Duke, if you grant our petition for aid,
it will not only help us complete our quest, but it will also secure your duchy from the ravages of the goblin horde for a season or more. Surely you can see the sense of that. (Makes a Diplomacy skill check and gets a success.)
Duke: Hmm, well said. I do remember the Battle of Cantle Hill. Nasty business. (The DM informs the players that the History skill can now be used to aid in this challenge.)
The narration of the success isn't in terms of the Duke being persuaded to help. It's in terms of opening up a new opportunity.
How about we stick to how they are defined in the rules... If you get X successes before Y failures you succeed at the skill challenge and attain the success goal. If you instead get Y failures before X successes you fail and are instead subject to the failure conditions... anything else is just stuff you're houseruling in.
Can you reference some rules text here?
DMG p 72:
The difference between a combat challenge and a skill challenge isn’t the presence or absence of physical
risk, nor the presence or absence of attack rolls and damage rolls and power use. The difference is in how the encounter treats PC actions.
Nothing here about absence of partial success or partial failure.
DMG pp 74, 76 (under headings about "Consequences"):
What happens if the characters successfully complete the challenge? What happens if they fail?
When the skill challenge ends, reward the characters for their success (with challenge-specific rewards, as well as experience points) or assess penalties for their failure. .
If the characters fail the challenge, the story still has to move forward, but in a different direction and possibly by a longer, more dangerous route. You can think of it like a room in a dungeon. If the characters can’t defeat the dragon in that room, they don’t get the experience for killing it or the treasure it guards, and they can’t go through the door on the opposite side of the room. They might still be able to get to the chamber behind the door, but by taking a different and more arduous path. In the same way, failure in a skill challenge should send the characters down a different route in the adventure, but not derail them entirely. .
Skill challenges have consequences, positive and negative, just as combat encounters do. . .
Success or failure in a skill challenge also influences the course of the adventure—the characters locate the temple and begin infiltrating it, or they get lost and must seek help. In either case, however, the adventure continues. With success, this is no problem, but don’t fall into the trap of making progress dependent on success in a skill challenge. Failure introduces complications rather than ending the adventure. If the characters get lost in the jungle, that leads to further challenges, not the end of the adventure.
I don't see anything there about the resolution of the challenge - including checks made, and narration thereof - having no effect on the outcome. In a 10/3 challenge to navigate through the jungle, for instance, it strikes me as obvious that the "more arduous" path would be different depending on whether the 3rd failure came after zero successes or 9 successes. And also that a group who arrives at the temple after 10 successes and no failures might be in better shape than one which arrives after 10 successes but 2 failures.
getting back his men has nothing to do with whether the set goal of the success state of the SC is attained (Unless of course it is the final success that decides it). It also does not mean he has a "partial success" since his goal is not to free his men but to return home and that is a binary outcome, either he does or he doesn't.
Under ths conception of what counts as a goal, could you give an example of a partial success? I would have thought getting only half one's men home might count.