Did you mean decide that your *character* knows it? (I'm assuming that you did, but the thread has gotten confusing enough I wanted to check.)
Oh, yes. Typo.
If the DM designed the world, then the level of knowledge that the people in it have about things is something the DM determines. Whether or not something has even existed in the world for example is up to the DM, and she would be quite within the authority we grant her by agreeing to play D&D to point out that a character from a world with no elves in is not going to have an encyclopaedic knowledge of Drow politics for example.
If there are genuinely no elves then it wouldn't matter whether or not a character claims to have encylopaedic knowledge of Drow politics. Some people on these forums probably would claim such a thing, and as far as I know there are no elves in the world, so I imagine a character in that world claiming such a thing would probably appear as haplessly nerdy to the residents of that world as....well, you know where I'm going with that. Why would the DM possibly care if the player described his character that way? If there are no Drow then there's no game impact.
If, on the other hand, the DM is planning to introduce Drow, perhaps gating them from another plane, then they do in fact exist.
The players have a say: the DM just has authority to overrule them. Do you grant the DM authority to describe what your character knows when you make an Intelligence(Arcane) check regarding an unusual symbol on the wall of a temple?
No, I do not. I grant him authority over what they actually mean in his game world, and I grant him authority over whether or not he has to tell me (and if he won't tell me then I'm going to have a really tough time roleplaying that I do in fact know). But his authority does not extend to what I know.
Let me reiterate that I'm not claiming this as the One True Way. I realize that a lot of people are happy with DMs dictating what they know, and what they dream, and whether PCs are allowed to Persuade each other, and whether or not they actually find the Warlord to be charismatic and inspiring rather than a self-absorbed megalomaniac. I acknowledge all that as a valid way to play. What I do *not* acknowledge is that that is the One True Way, either.
That can be a real hassle, particularly in the case of where a player has preread the adventure path the group is on and decided that as the final arbiter of their character, their character "knows it". Then its perfectly in character for their character to know it. If you see what I mean.
Here are two more things I acknowledge:
1) There are such things as "cheating", "being a jerk", "ruining the fun for others (and yourself)" etc. But those exist regardless of where you come down on roleplaying, player agency, etc. So using examples of being a jerk to defend a certain mode of roleplaying is avoiding the deeper question entirely. You may play at a table where buying a silvered short sword to go werewolf hunting is considered to be breaking character, and would therefore spoil the fun for others, in which case you shouldn't do it. But that doesn't make it "bad" roleplaying.
2) Modifying adventures so that the players are genuinely in suspense, rather than pretending to be in suspense, is definitely more work for the DM. And 100% worth it, in my opinion. I find pretending to not know things to be a completely dull form of roleplaying, especially if I know everybody else at the table is pretending to not know the same things, and I won't ask my players to do it. YMMV.