I agree that there is a concession here. But that should be clarified in the wording. I tend to use "You know" or "Your character would know" for things that are obvious common knowledge--in this setting there are two moons, one red and one white. Things like that. These things are clear-cut and always true. I use "You think/you've heard/you've been told" for things that come from in-game sources (and could be false), such as the result of INT checks. Things that come from NPCs are flagged similarly. "It is commonly believed that" is for rumors and hearsay--things that are very fallible.
The agency denial comes in stating setting truths as untruths or the reverse. When the DM denies information that's needed to make an informed choice (by commision or omission), especially when done with the intent to cause the player to make a different choice, they're at least partially denying agency.