Really? So whenever I suck at a game I have no agency? I need to use that excuse when I lose!
It is a binary. Either you have agency or you don't. If you want to talk more or less agency, then it gets very subjective. What you view is more agency others will view as less and vice versa. Because of that subjectivity, I focus on whether you have it or not.
To you. That's your subjective opinion, except for the part where blind choices are not an example of agency. You are just wrong about that one. You still have agency, it's just not enough subjective agency for you and you want more of the kind of agency that you like. There's nothing wrong with wanting more of the kind of agency you like, but telling others that they don't have agency at all in those situations is wrong. Your dislike of the amount of agency you have in those situations doesn't translate into it not being there for either you or others.
The bolded is the problem here. Meaningful is nothing BUT subjective. I find there to be meaning in the blind choice between A and B. You don't. That's fine. The issue is that you are incorrectly trying to say that there is no agency in the latter situation just because you don't find subjective meaning there.
It doesn't take ANY information to allow for some agency. It's just less meaningful to you than you like. To take agency away from someone to the point where they have none, they need to have no ability to make choices other than those the DM wants them to make.
They are the same, though, when the DM can unilaterally make any change he wants at any time he wants. If the DM doesn't have total authority and/or cannot make any change he wants to the rules, then it's not Rule 0. It's whatever rule the game gives the DM or table to change a rule under limited circumstances.
Because if you don't trust the DM, you should not be playing in that game. You will very often be disruptive to the game, interrupting to ask why something was done or arguing over something. Lack of trust destroys games. When I go into a new game I give the DM trust and it stays there until he shows me that he is not deserving of that trust, upon which time I walk out of the game.
Trust is also granted. If my house is on fire and firemen show up, I'm going to trust that they know what they are doing. I'm not going start questioning them for why they are doing certain things because I don't trust them. They are the experts in fighting fires.
The DM is presumably the expert in running the game, unless I KNOW that he is new. Even if I know the DM is new, I'm not going to distrust him, but I will be on the lookout for possible mistakes and be ready to offer quick friendly advice if it's a major mistake, or friendly advice after the game about what I saw if it wasn't major.
Rule 0 is a cornerstone of traditional play. Rules changes to make the game better has been a large part of the game since its inception.