Well, that was easy, eh? But what is agency?
As noted, this is a somewhat philosophical point in role-playing games. In video games, the code is quite explicit about what it allows and does not.
"Agency is an experiential pleasure. As such, it can fade in and out; it can fail altogether. Agency is not automatic, and so simulated environments should be cleverly constructed to help users/players get there." - Steven Dow (2009)
If a choice is made without information, then the results cannot be predicted.
A tabletop role-playing game consists of Infinite Play. There are no impassible walls, the most minor guard can be talked to, nothing is pre-programmed.
If you remove the ability to access information, you are restricting agency. It is information and the players ability to gather it that allows them to have an expectation of the results of their actions. This allows them to form an intent to act on.
"This process of accumulating goals, understanding the world, making a plan and then acting on it, is a powerful means to get the player invested and involved." - Doug Church, Formal Abstract Design Tools 1999
Are you against each other? Opposed?
If the player believes so, then she might refuse to explain her idea. Her stance is "The Dungeon Master will invalidate it because he wants to win!"
If the Dungeon Master believes so, he will change the rules to get his way. "I spent time on this. They want to ruin it!"
Neither is true, partisanship is the problem. Both parties desire to play, but while being respected. I talk at length, concretely, about how to address this impasse.
"[I]n [computer] role-playing games often the best uses of consequence come when they are attached to intentional actions. . .when these tools work together, players are left feeling in control and responsible for whatever happens." -Doug Church, Formal Abstract Design Tools 1999
The feeling of empowerment from agency must be an illusion. It is subjective ("a feeling") and unrelated in fact to whether the choice is actually a real one. (ref: Illusionism)
That said, bad practice is bad because it works poorly. Actually providing true individualized consequences to choices is the best way to engender the feeling of Agency.
Action alone is not agency. Moving a game piece, deducting damage, rolling dice are all actions that have effect. But they are not choices related to the player's intention. They are the results of a choice that may or may not have agency. The actual "play of the game" is just finding out what happens after the choice has been made.
The struggle is to insure that the choice made provides agency.
"Agency is the satisfying power to take meaningful action and see the results of our decisions and choices" - Murray, J. Hamlet on the Holodeck. Free Press, New York, 1997.
Games are designed, meaning they create via their structure the activities they encourage the players to engage in. A game is well designed both when its structure satisfies the desire for agency and when it is able to communicate this structure to the player to manage expectations.
Players come to play at the table with assumptions about what play will involve. To be successful they must transition from their initial assumptions to an understanding of what play actual does involve.
"A player will experience agency when there is a balance between the material and formal constraints."- Mateas M. A Preliminary Poetics for Interactive Drama and Games 2001
What this means is that the structure and design of a game and the choices available within it communicate information to the player that allows them to make an informed choice of action with a consequence that reflects their intent. (whew)
A multitude of options and choices is not necessarily agency, any more than a highly structured game with limited choices denies it. "Story" is irrelevant to agency. Anything that needlessly disrupts this interplay, disrupts agency. Adding in material constraints (Here's a new skill, basketweaving!) that isn't related to the formal constraints (Gold translates to experience which raises your power) diffuses the focus of the game, resulting in a reduction in agency.