Finding traps is a saving throw, and works as such.
Thus, anyone can interact with the fictional world and discover or avoid traps purely by investigation and reason. Note that this doesn’t necessarily require any particular mechanical knowledge on the part of the referee or players (though you can go there if you want), it just requires determining trigger mechanism, effect, and clues. Remember, traps don’t need to be mechanical, or even explainable. Traps can be driven by magic, ancient technology, or incomprehensible clockwork.
I think this is really a special case of a more general principle. In some sense, all of combat is also a (complicated) saving throw. If, through smart play, a player can figure out a way to defeat or slay their enemies without a single attack roll, good for them. (Some examples: luring monsters into a trap, flooding a room, burning down a structure rather than engaging in an encounter, starting an avalanche to bury an enemy encampment, ad infinitum.)
— open locks by picking or foiling magical closures
— remove small trap devices (such as poisoned needles)
Thieves — are humans with special abilities to strike a deadly blow from behind, climb sheer surfaces, hide in shadows, filch items and pick pockets, move with stealth, listen for noises behind closed doors, pick locks and remove small traps such as poisoned needles.
AD&D Players Handbook; 1978 (page 27):
Finding/removing traps pertains to relatively small mechanical devices such as poisoned needles, spring blades, and the like. Finding is accomplished by inspection, and they are nullified by mechanical removal or by being rendered harmless.
They are the only characters who can open locks and find traps without using magic to do so. Due to these abilities, a thief is often found in a normal group of adventurers.
Find/Remove Traps: The thief is trained to find small traps and alarms. These include poisoned needles, spring blades, deadly gases, and warning bells. This skill is not effective for finding deadfall ceilings, crushing walls, or other large, mechanical traps.
You can find secret doors, simple traps, hidden compartments, and other details not readily apparent.
The Search skill lets a character discern some small detail or irregularity through active effort. Search does not allow you to find complex traps unless you are a rogue (see Restriction, below).
Restriction: While anyone can use Search to find a trap whose DC is 20 or lower, only a rogue can use Search to locate traps with higher DCs.
So this idea of find traps as a saving throw is clearly a recent innovation, but it could be thought of as a refinement of the early OD&D approach where there was no find traps ability and remove traps could only be used for very small mechanical devices. The find traps ability does not show up until AD&D. In both OD&D and AD&D, susceptible traps are very specifically defined (small devices), and this is perpetuated in 2E. Moldvay doesn’t define traps at all (perhaps leading a generation of gamers to think that hazards like the the rolling boulder of the Indiana Jones movie could be discovered and disarmed with a simple throw of the dice). And then 3E decides to do away with qualitative differentiation all together and replace it with a continuous difficulty class rating.