Maybe it wasn't clear what I meant by "secret backstory" - I don't mean that the GM has ideas about the backstory that the players don't know; but rather that the GM relies on that secret backstory to adjudicate outcomes of action resolution (as in your example of play). I think an RPG absolutely can work without the GM relying on secret backstory to adjudicate outcomes. I know that from experience.
And I get this. I just prefer having the framework in play and only changing it if the PC or NPC actions should modify it.
I do not like modifying it, just because the players ask for an unexpected dice roll.
There are a range of ways to adjudicate an RPG, which straddle rules techniques and approaches, and a good DGM will discuss them.
I don't fully get your first example - but if the PCs are already in a trapped room and have triggered the trap then I don't think I'd be mucking around with Perception checks. I'd be narrating the threat posed by the trap.
The example was meant to be a repeat of the original example.
In the spaceship incident, the PCs had already gotten on to the space ship. They had not yet set off the trap (that occurs 100 miles off of the ground due to an altitude trigger) and could not find it in the space ship without special abilities (e.g. special powers like x-ray vision), but they were no longer outside of the space ship where they could check out the security cameras. Normal searching inside the space ship would not find the bomb.
In the trapped room example, the PCs had already gone into the room. They had not yet set off the trap (that occurs when 3 of them are standing next to the altar) and could not find it in the room without special abilities (e.g. spells like Detect Magic), but they were no longer outside of the room where they could find the control mechanism to turn it off. Normal searching inside the room would not find the magical trap.
Same basic scenario, different genre.
As a DM, in both of these cases, I do not allow the perception/search to find anything. I do not allow the scenario to change, just because a player asks to search. A PC could go back outside the room (or off of the space ship) and find the key to the problem, or a PC could use special abilities (the wizard can cast Detect Magic, but the searching rogue might not have that ability, or a different superhero has super smell and can smell the C4).
As for your second example, what's illogical or implausible about finding a blood drops, or a dropped neckerchief, or something else on a cobblestone road? There are things to be said for and against "fake changes" (although that's not a neutral description of the technique), but verisimilitude, or plausibility vs contrivance, in my view Isn't a very helpful way to talk about it, because nearly everyone treats verisimilitude as a constraint on narration. Someone who, in response to a successful track check on the cobblestones, narrates a dropped neckerchief doesn't regard that as lacking in verisimilitude - the narration of a dropped neckerchief as opposed to (say) a dropped gilt-handled dagger is precisely intended to preserve verisimilitude.
There's nothing implausible about finding blood drops, or a dropped neckerchief, or something else on a cobblestone road.
What's implausible for my gaming style is that because a player wants to roll a tracking roll, reality suddenly shifts and because the player rolled high on a dice roll, that neckerchief suddenly mystically appears on the road.
As a DM, if a player asks for the tracking roll, I like to decide right there and then if there is anything to find, before he rolls. If there is a decent reason for something to be there, sure roll. But if there is not a decent reason for something to be there, I don't like having to shuffle my vision of the world to suddenly include something there that logically should not be there. I also do not like giving a roll, the player rolls a 20, and then I have nothing to give him. I'd prefer to tell him that there is nothing there and have no roll than for him to roll high and then either I tell him he does not find anything, or I make up some last second BS on the fly just because he rolled high.
It's a style difference. Some DMs say "yes" to anything.
Player: "I'd like to see if I can track the blacksmith"
DM: "It's a cobblestone road so the DC will be high."
Player: "I rolled a 20, so 27."
DM: "Ok, you see a tool lying on the ground over by the alleyway. You are not sure of the type of tool, but it is long and awl-like with scorch marks on the end."
I do not prefer this DMing style.
In other words, I like to decide when to "just say yes" and when to not do so. Depending on the scenario, I will be either more or less generous in handing out information. I am not always generous, especially if the scenario is one where information is unlikely to be found. I do not like being forced to hand out information in an unlikely to be found scenario, just because a player asks for information.
A more "just say yes if it makes sense to do so" approach than a "just say yes all of the time" approach.
Alternatively, I like to set up adventures with flowcharts (maybe not actual flowcharts, maybe just some notes written down). Multiple different ways to get to an event (location, encounter, etc.). Multiple different directions to leave from an event. Multiple different clues possible to be found at each event (some easier to find, some harder). Sometimes, the clue is harder to find because the DC is harder. Sometimes, the clue is harder to find because the DC is lower, but the players have to go out of their way to go find the clue. The security camera situation is one of this type. But no clue is essential to the adventure. Some are found and followed, some are found and not followed, some are found and misinterpreted, and some are never found. No event is essential to the adventure either.
As time goes on, more and more flowchart events are added to the campaign (or entire mini-adventures are added) as the framework of the campaign is fleshed out. Some of that fleshing out of new events comes directly from the ideas / goals of the players. Some is not driven by player/PC motivations or goals, it's just new parts of the world that the DM just came up with.
PS. As a player, I dislike it if the DM corrects the players on the misinterpretation of a clue as well. If no given clue is essential, then interpreting it correctly is not essential either. There are some players who absolutely want their interpretations of the information that the DM supplies be 100% correct. I don't need that or want it unless it's the DM misstating what we see (i.e. he is the window to his world, so it should be a clear view). But if the DM states it correctly and we just misinterpret its value or meaning or come up with the wrong conclusion about it, then the PCs should be allowed to go down the wrong path.
The concept of "just say yes" seems to go hand in hand with "make sure your players are 100% clear on everything" type of approach. No. Mystery is fine and welcome, especially if it is mystery caused by player interaction/faulty conclusions and not just the DM foobaring. Some players hate this. but I sometimes like it when we screw up because it often leads to unexpected and off the beaten path situations.