This goes right back to the OP where the question was about the difference between what your character does, as in proposes an action that the DM then determines the result of, or what you character does, as in you get to say the action and the outcome. This is firmly in that former group, the thin declaration, whereby the player is essentially asking the GM to do something nice if they succeed at the mechanic (that the GM likely picks, and sets the parameters of).Not quite, in my view.
When the roll shows 'success' the GM is bound by that to narrate a successul outcome...of some sort. This successful outcome doesn't (or at least IMO shouldn't) necessarily have to directly match what the player had in mind* as long as the narration reflects an overall success for the PC.
My example above, though not the best, tries to show this: the search doesn't find the incriminating financial records the PC was looking for but does find something else that's every bit as incriminating: the Southtor seal, which no loyal noble would normally have anything to do with. Specific goal of finding financial records: not met. Overall goal of finding incriminating evidence agains tthe Duke: met in spades.
* - though most often it will anyway, as much of the time the success-failure outcomes of a given action are fairly obvious.
This gets back to our old argument regarding what 'failure' represents; here you'd have a failure just become a different type of success, which isn't a failure at all.
to go back to your earlier example, you swapped out papers showing guilt for a seal that may show guilt. Assuming that the result of the find aren't already in the GM's notes and the GM decides this at the moment, this is a weakening of the play the player does -- the GM is reducing the level of success to something that the player wasn't asking for. Yet, it's presented as a good because it doesn't fetter the GM from softening outcomes like this and fettering the GM is... bad, I guess. It's also presented as if the softening of outcome is a good as well -- that's it's cool to reduce the asked for success because the GM wants it that way. This thinking, to me, goes hand in hand with structured GM stories that the players play through -- the GM is acting this way to protect their idea of what should happen rather than playing to find out. It's a valid way to play, obviously, and popular, also obviously, but it really puts the entire load on the GM to run in a principled enough manner to keep players. Judging by the many threads, this may not be the most common outcome.