Or, a third option, play their character as if the character is something like a real person with knowledge separate from that of the player.
We don't seem to have any difficulty with the idea that characters in horror rpgs, such as Call of Cthulhu, are unaware of the existence of the supernatural. They all have to start off as Scullys.
This isn't a third option though. It's still the DM directing the players to play to the best of the DM's story, which involves them being ignorant of things the players actually know. This isn't high art -- it's lazy. It's lazy on the part of the DM.
And, you can tell because if a player declares that their character does know about trolls and fire, or the supernatural in CoC, the immediate reaction of the DM will be to challenge this and require justification. Justification that's not required for any other decision of the player in regards to their character. And, this call for justification is because the story the DM has envisioned will be harmed if the PCs can actually address whatever gimmick is being hidden by the pretended lack of knowledge.
Let me put it another way -- the first time you met a troll in game, it was cool. You didn't know about the fire and the encounter was scary and very interesting. Now, the second time you meet a troll, you have to pretend it's cool. It's not actually cool. The only fear is worrying how long or how much damage you have to take before the DM will let you use fire. This isn't achieving the goal of cool and interesting play -- it's just justifying the DM's laziness and forcing their preferred story outcomes.
And, I'll quibble with you on CoC. It's not that the PC can't know about the supernatural -- they very well can be firm believers in the weird and not lose anything. It's that knowing won't help. Call does this very well where even knowing things can be worse than not. It uses knowledge in a distinctly different way.