It's like saying that, when given the option between two glasses of milk, one spoiled and one not, that it doesn't matter if you're told what the expiration dates are or that one smells bad because you still have the option to drink either one.
I don't find it to be even remotely like that.
I think that you are advancing the idea that since the player can choose to ignore the information (itself a dubious claim) and choose however they want that the information isn't important.
Actually, I come at it from the other side - the information isn't necessary in order to arrive at the choice, so worrying about whether or not the player has the information is attempting to police the thoughts of the player, rather than police whether or not the character is doing something they shouldn't be able to.
It is a classic case of the phenomena by which trying to avoid metagaming results in metagaming more often than not, in my experience, because it only raises any warning flags to people that are concerned with the idea of "metagaming" - because they are on the watch for the character using information the character doesn't have, they completely disregard whether or not the character's actions actually
require any particular knowledge, and end up forcing the character's actions to be determined explicitly by what the player knows.
For example, to try and clarify because I know you have trouble understanding me, let's look at two scenarios:
Scenario A) Jim, who has never played D&D or any other table-top RPG at all before tonight, is playing Regdar the fighter. As he is cautiously proceeding into a dungeon, he comes to a side hall. Jim knows from the brief spiel given to him about what kind of stuff happens in a D&D game, and how he can describe doing whatever he wants and the DM will tell him what rolls are needed if any, that danger could lurk around the corner. So he says "Regdar creeps up on the corner, hugging close to the wall with his great sword gripped in both hands. He rounds the corner swinging the sword, swiping at the monster he assumes to be there."
Scenario B) George, who has played at least a few campaigns of D&D, is playing Regdar the fighter. He is also cautiously proceeding into a dungeon, and comes to a side hall. George's DM calls for a stealth check, which George makes and reports the result of. He then says "Regdar creeps up on the corner, hugging close to the wall with his great sword gripped in both hands. He rounds the corner swinging the sword, swiping at the monster he assumes to be there."
If Scenario A is acceptable, with Jim having no idea whether a stealth check has been made in secret by the DM or has not been made at all, and Scenario B isn't acceptable specifically because George has the knowledge that there was some reason for a stealth check, then is it not
player information the character doesn't possess which is determining the character's action (or, to be more accurate, that the character can't do that particular action)?