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.
Yes, which is my point, qualitatively different things
are different things. When someone says that there's 'just as much agency' in one game as the other, they're trying to argue that 2 different things should be called the same thing. That isn't useful analysis, in fact its obfuscatory.
And nobody is arguing that all games are the same or need be the same.
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);
The GM-centered game answer, player has no agency over the fiction here.
2. There isn't one (as determined by a die roll); or
Which is only really compatible with some sort of player fiction agency, since presumably there's a possible positive result where such a thing does exist.
3. There isn't one (as determined by the DM on the spot)
Why is this different in any real material sense than #1?
4. There isn't one (as determined by the player deciding that there shouldn't be one there).
I would expect that the possibility wouldn't even have come up then, in which case we can assume that in the player centered type of Story Now game this implies the player is already suitably engaged, or wants something else. In either case the GM wouldn't introduce such a secret door here, and shouldn't.
Those are all different mechanical rule approaches but the result is the same.
I see fundamentally 2 approaches here.
1) The GM is in absolute control over what elements can be added to the fiction, a secret door (or anything else) only exists when he says it does.
2) The player is able to suggest or add elements to the fiction, or change the fictional positioning, in ways that are beyond or aside from what the character could do. This is usually a result of spending some resource and/or making some kind of check, but the exact details depend on the system in question.
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.
Yes, it is, as I've just explained above
#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.
You aren't even having a discussion at the same level then. We're not talking about a specific set of rules. This isn't a discussion about player agency in B/X Molday (to pick a 'classic' ruleset). This point #1 you have brought up is only meaningful in relation to other possible ways to play, if you only compare a play technique to itself and then declare that it doesn't do anything different than its own self, this is what I would call a 'tautology' and kind of a waste of column inches!
#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.
Of course it impacts player agency, WRT #1 massively. The player now has an entire capability to express influence over the content of the fiction! To make this statement as you do seems literally nonsensical to me! Its like saying "here we have this orange, but its just an apple!" in direct contravention of what is readily apparent right on the face of the thing!
#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.
Again, this is just #1, and the same comment applies. The 'room for abuse' comment is not really relevant to this particular discussion (though it might bear discussion in the larger context of the whole thread).
#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.
Again, this isn't coherent or meaningful. Why would the player be checking for a secret door he has no interest in finding? What relationship to player agency would finding things he's not interested in have? There's nothing to this point at all.
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.
Well, now I'm not understanding what you're saying. You SEEM to have claimed that there's no issue of player agency at all with #1 and #2 and that somehow they are the same, but they are in fact the 2 possibilities of a binary choice, the GM determines all fiction, or the GM doesn't determine all fiction. Here you seem to be speaking as if you fully understand that, yet you dismissed it a moment ago! If the player's ability to add to the fiction does not represent a field of player agency which does not exist if the GM disallows it, then how can the GM possibly take away player agency?