To the extent that this is an interesting question (and it is), and to the extent that it keeps popping up in threads (and it does, as an analogy), I think it helpfully illuminates three different styles of play.*
In the beginning, there was the idea of "skilled play." If you look back, you see that while players inhabited a role (proto-roleplaying), players were also assumed to have some skill at the game itself. That is why early modules featured puzzles and traps and riddles and so on that were meant to be solved by the players, not the PCs. And the different abilities of monsters were known (or not) by the players, not the PCs. This was so well-known that one of the earliest Dragon Magazines (before the Monster Manual!) mocks the problem and has a way for DMs to create random monsters!!!
Then we can discuss the concept of "role playing." People that were more interested in role playing became focused on the divide between the player and the PC. The player might know that a troll could be stopped by fire (having encountered one in the last campaign), but the PC might not. So the player would have to determine if the PC had that knowledge- did their history, background, intelligence, and so on, mean that they would know this? Would a noble-born Cleric know it? How about a peasant fighter recently released from the army?
Finally, there is the concept of "dice play." With the advent of later parts of 2e, and especially 3e on, their was an increased emphasis on the use of dice to resolve non-combat situations.** Here, instead of looking solely at skilled play (what the player knew) or the role play (what the PC knew), the player would determine if the PC knew that information the same way that the player would determine if the PC hit an opponent; by rolling. This made it worthwhile to invest in an applicable skill to know, um, stuff.