We're still talking about different things. [MENTION=42582]pemerton[/MENTION] has stated it pretty explicitly a few times, "agency over the issues they engage within the game" to paraphrase. As with my 'spherical cow' above, the endless maze, if the only choice is left to face orcs and right to face undead, that's SOME agency over the activity of the characters, but it is a SMALL agency because it only allows choices with the absolute bounds of what the GM proposed. A player cannot say here "I try to find the secret passage which leads to the land of the Yuan Ti, my character is obsessed with finding them."
But they still have 100% player agency in both scenarios. What that agency allows them to do is different, and that's my point. The "issues they engage within the game" is dependent upon the rules of the game.
In your spherical cow example, the player
can say "I try to find the secret passage which leads to the land of the Yuan Ti, my character is obsessed with finding them." That doesn't mean he'll find it, though.
Of course, if we explore that a bit farther, the answer might be no because:
1. There isn't one (as pre-determined by the DM);
2. There isn't one (as determined by a die roll); or
3. There isn't one (as determined by the DM on the spot)
4. There isn't one (as determined by the player deciding that there shouldn't be one there).
Those are all different mechanical rule approaches but the result is the same.
Player agency itself isn't any different for any of them. They still have full control over the parts of the game that the rules allow. However, they allow different levels of control of the fiction outside of their characters.
#1 doesn't impact player agency, because in that system of rules, the player doesn't have the ability to influence the placement of a secret door. The DM could impact player agency by lying, even though he had placed a secret door there.
#2 doesn't impact player agency, but it does allow for the placement of such a secret door with a successful die roll. Note that the DM could affect the player's agency through modifiers.
#3 doesn't inherently impact player agency, since the rules allow the DM to decide whether a secret door is present or not. But there is certainly room for abuse, depending on how the rules.
#4 is the only option that puts the player fully in control of the decision, by the rules. The DM might be able to impact player agency by overruling it, but if the rules give the player this capability, that's probably not an easy option for the DM.
Of course, many might indicate that it is within the rights of the DM to overrule any of these, and it was explicitly stated in the AD&D DMG, but most would agree that this is wrong and takes away the player's agency.