Like let's examine this think/know divide with another lovely practical example.
The module says "On a successful DC 20 history check a character can identify the carving above the entrance of the dungeon as the seal of King Tharguz and recall that said king ruled the are three centuries ago and was killed in an uprising that started by the rumours of the king dealing with the devils."
Would it be acceptable if after failing at the roll the player picked up the module book, looked at the page and declared that their character thinks that the thing above the door is a seal of King Tharguz who was rumoured to be dealing with devils? Do you really think that the makers of the game intended this to be a valid way to handle this?
Do you really think that's what we're talking about? Or is that an unrealistic and extreme caricature of it that you've devised in order to prove us wrong?
But, sure let's look at that example: the player does exactly what you describe. But I want to add one element: this information about King Tharguz is important. It's either the key to, or at least it is in support of, completion of the adventure. Somehow knowing this fact will enable them to declare an action later that helps them with their goals. (Otherwise it's too easy to dismiss it as not mattering.)
So this player opens their copy of the module and reads the text aloud. I won't even pass judgment on whether or not the player is being a jerk. Let's just see what happens.
Well, with everybody rolling...probably with Guidance and/or taking the Help action...there's a decent chance somebody is going to get lucky anyway. So clearly having somebody know the answer is one of the acceptable outcomes. And I would even say it's a desirable outcome. So let him/her have it. In-game, one of the characters knew the answer (and maybe even the lowest Int character, the explanation of which is a great opportunity for roleplaying). So everybody at the table looks at that player strangely, wondering where they picked up their D&D playstyle, and the game continues.
Great. Our playstyle survived this unrealistic stress test. I can't imagine this ever actually happening, but if it did, there's no real impact.
Now it's my turn to interrogate your playstyle, similar to the way I did before, using the same situation.
Everybody fails their lore test, so they forge ahead into the dungeon. When it gets to the moment where the information about King Tharguz would suggest a particular course of action, one of the players does
exactly the right thing.
If you ask the player why, he/she shrugs and says, "I dunno. It just seemed like a cool idea."
And this isn't the first time this has happened.
What do you do?
P.S. And let's also think about which of these scenarios is something more likely to occur at the table. A player reading aloud from the module, or a player coming to the game with information about the module but not telling anybody?