Swarmkeeper
Hero
Yes, I did read your statement. To be clear, either way the result is that nothing has changed in the scenario. Not an exciting outcome for a success or a failure, IMO. In our game, the dice are not used to hide things from the players. The dice are used to resolve actions that happen to have a meaningful consequence of failure. If that is too RAW for you, I get why you needed to come up with some other mechanic under the rubric of "DM ruling".To-may-to, To-mah-to. 5E really isn't useful with RAW, since it's designed to be based on DM ruling. Because of this, the only people I've found that focus heavily on RAW are those who want to find an exploit to argue. YMMV.
If you read my statement, it's not "you still don't know" it's "you're positive there is no [X]." I'm not a fan of it, but it solves the issue presented while using RAW.
As an aside, I try my best to not tell the players what their PCs think. So, really, both of these statements - "you still don't know" and "you're positive there is no [X]" - are phrases I try to avoid in our games. My adjudication of a roll describes the new state of the scene. How the player decides the character interprets that result is up to them. I find our games flow more smoothly with the DM sticking to environment and NPC/monster description and the players determining what their PC thinks, feels, and does in the context of that environment/NPC/monster.
Mathematically, if you take the DC the PC would roll against and subtract 12 to create the modifier, the odds are the same if the roll is made against the passive score. If the PC has a +5 Wis/Perception, they'd succeed on a 10 DC 80% of the time (roll of 5+). Their Passive Perception would be a 15, which sets the DC for the trap/door/whatever. The DC: 10 would have a -2 modifier that would succeed against the 15 Passive DC only 20% of the time (roll of 17+), which is the percentage the PC would fail.
Based on your playstyle of using the dice to add mystery, I'm now understanding why you'd need to inject this math into the game. I'm sure it has become second nature for you and works well at your table. Something like that is unnecessary in our games, though.
So I'm still curious why you would decide to roll a die during play for the "hiddenness" of a trap or secret door, which are inanimate objects. Can you say more about that?