Crimson Longinus
Legend
Let's examine illusionism. I offer you the appearance of a choice, but, no matter what you pick, my preplanned encounter occurs. A specific example would be the I have an encounter with orcs planned, but ask the party how they plan to traverse the Dark Wood. The party can choose to move quickly, hoping to avoid encounters, but get orcs. Or then can choose to sneak through, but they get orcs. Or they may decide something else, and still get orcs. From the player perspective, the choice they made appears to have weight, but something bad happens. They cannot tell that their choice is meaningless. According to your argument, here, they have as much agency as a party who's choice do affect what they encounter -- if they sneak, then maybe no orcs, for instance. I disagree this is the case.
To further this, the players involved could find out that the GM forced the encounter, about as easily as a person might find out a lie. In this case, the situation is exactly the same as a lie discovered. I also disagree that lies are objectively discoverable as a trait. Some are, some aren't.
That was a rather awkward use of illusionism and thus a poor example, but ultimately it doesn't matter how the engine runs behind the curtains. In an style which relies heavily on improvisation the difference between illusionsim and making up naughty word on the spot is murky and not worth agonising over. If the players feel that they're making meaningful choices then that's good enough.