Trying to find an objective RAW is pointless
Both of these summarize my opinion nicely. RAW is only useful for rules lawyers seeking an edge, which can include DMs. In the case of Organized Play (currently AL), either the DM will make a call at the table or the organizer already has a listing of specifics, such as Sage Advice.throw your precious RAW in the dumpster.
An alternative option, which I lost from an earlier draft, is a certainty check. The character makes the check to be absolutely certain there isn't a trap/door/creature. It's not a very useful check for the characters, but it's legitimate under RAW while keeping the players uncertain unless they succeed on that check. As using a resource on this kind of check feels bad for the player, I'm loathe to use it, but it's RAW as opposed to my earlier option (which the player would likely prefer).This is antithetical to the 5e rules around ability checks. If something is impossible, there is no roll. The stated action just fails, Knack or not. (PHB p174 and DMG p237)
And:If the players see their roll (some DMs choose to keep it secret) and know they rolled high, they may have a good idea that there are no traps, but they do not know for certain.
Last week, our rogue rolled a 16 when checking for traps. Knowing that most traps are DC 15, he strode confidently forward. This, particularly well concealed trap, happened to be DC 20...
This is why DMs should use Passive checks more often. When the party is moving down the hallway in a dungeon, I make rolls against their passive perception by traps, secret doors, hidden monsters, etc. This prevents the players from being aware, especially before it's too late in the case of traps and monsters. Only if a player specifically mentions a location they want to check do I call for an active roll.To give an example of what I'm talking about, you telegraph a trap several rooms before the trap itself. The players declare they are searching the room, you tell them there is no trap. They declare they are searching the next room, you tell them there is no trap, they declare they are searching the next room... you tell them to roll.
Immediately, before they even pick up the dice, they know the trap is in this room. If they fail, and you tell them they don't find any traps, they know the trap is in the room.
Since I'm bringing it up, and usually people ask why I'm rolling on Passive checks, there are no actual rules in the PHB and DMG about how to use Passive skills, except in the use of Hiding. The default assumption is that the passive is the lowest you can get (a carryover from 4E considered "official" by Crawford), which is why no one likes to use it. It creates a static number check, with either an automatic pass or fail, which is boring and stupid. Mearls once suggested that the things opposing the Passive score should roll instead, just like attempting to Hide. This keeps the players from meta-gaming the results.