The rules are explicit that Intelligence is used for accuracy of recall, education and memory. If the character needs to recall a key piece of information about monsters, this is something covered by these rules. Recalling ale might have a DC of 5, so even a very low intelligence creature can do it passively.
However - ARCANA specifies it is use to recall lore about planar creatures. NATURE is there to recall lore about plants and animals. These are examples of how it is to be applied - when you want to recall something you use these skills.
People complain that intelligence is a dump stat because they don't use it how it was designed - to be the thing you test when your character, as opposed to you, knows something about their enemy.
Alternatively, you might consider whether the rules are actually different than you see them.
Player (I literally did exactly this two days ago): "I study it closely...without touching it...to see if it's a real green slime, or just slimy green moss?"
DM: "Roll Int"
I failed, badly. (Was getting assisted by another player, rolled 2 2's, and since I have 8 Int I ended up with 2 1's.). So I decided to conclude that it was a green slime, and that I "recalled" that green slimes can leap 20', so I backpedaled and watched it suspiciously from 25' while the other players searched the room.
Now, I haven't seen a green slime in a long time, so I actually couldn't remember what they do. Are they the slimes that destroy your weapons, or the ones that eat your brains?
Let's say I "remember" that they are the ones that destroy your weapons. I can proceed with that knowledge. I could be wrong, either because I really am wrong, or because the DM or the adventure changed things up, or because I mis-identified the monster.
But, instead of relying on my memory, I might say, "I wrack my brains to see if I can remember any stories about what green slimes do." And, again, the DM might ask for a roll. And that would be using the rules as written, as you mention.
In both cases those actions are perfectly in line with the rules, as written. Nowhere...NOWHERE...do the rules specify the narrow application that you are describing. There is no rule that dictates or constrains what players may decide their characters believe, or not believe.
D&D is a role playing game. It is always a game. It is always role playing. When we play a role, we must pay heed to the limits of the role. When we give the role our capabilities, rather than those inherent in the role, we are not role playing. We are role ignoring.
I'm willing to concede that there are multiple kinds of roleplaying, and all are valid (even if I find some of them rather dull and uninteresting.) But since you seem to be unwilling to grant the same, and insist that my sort is not roleplaying, let me turn that around:
When you are pretending to not know something that you have decided your character doesn't know, you aren't actually inhabiting your character, since your mental states don't align. Instead you are merely
acting.