The ratchet turns toward remembering-- in general use the better memory of player and PC
You have two cases running in opposite directions. In each case, only one outcome is generally considered "fun".
Note-taking players with good memories:
If the players are so engaged in the game as to be doing hard work like taking notes (or are simply paying enough attention that they are remembering bit characters or throw-away lines, how exactly would a GM benefit by punishing or failing to reward that engagement?
Sure, you can concoct some reasons, like that you think a comedy of errors or identity confusion would be a fun thing to play through, but the fact of your players engaging in the details that strongly really suggests otherwise. No one takes notes on something so he can have someone else arbitrarily decide they cannot be used.
(Somewhat as a side note, those who take notes are gems among players; those who make their notes available to the GM are doubly so, as it provides the GM a separate and independent memory and gives a huge insight into how the players are taking in a plot line. In my experience, one wants to encourage this behavior as strongly as humanly possible. If that means letting them refer to their notes during the game, so be it.)
Poor-memory players with normal memory PCs
This is, as you note, exactly the opposite situation, but it still leads in the same general direction. Most players will not go to the effort of keeping detailed notes on a game, as in the prior situation. And the players, as opposed to the PCs, are not living through the experiences, they are hearing condensed verbal summaries. It is reasonable to assume that even non-eidetic memory PCs will have clearer memories of things than players.
I do like to see players paying attention, but I realize the limitations of the human memory system. Not only am I not inclined to punish it, I am inclined to generally help the players out as long as it isn't getting too disruptive and as long as I don't think I'm unintentionally encouraging them not to pay attention.
I find the benefits are two-fold: First, the narrative usually flows more smoothly if the players and characters are not stumbling in-game through mistaken and misremembered identities; second, the players tend to feel less foolish (I do when I am a player in that situation) when their memory is not constantly an issue, and they will enjoy the game more... and therefore so will I.
I think, however, there are more reasonable special cases on this side of the coin: Obscure NPCs who were just hanging around in a background a year ago, meeting a great many NPCs briefly but in rapid succession, etc, these are all fairly taxing things. I might in some cases allow a roll to help the player, but I would never take away or disallow something a player remembered on his own.
(Which roll? Again, I am inclined to extreme generosity, here, and all three of the non-physical stats has a case to be made: Intelligence is recall, wisdom is attunement to the environment, and charisma is people handling. I would be inclined to let the player choose, actually.)