There are two different trap mechanics presented in Moldvay's Basic D&D rules, the general one that uses 1d6, and the thieves' ability that uses d%. The reason for this, although it is far from obvious, is that the game distinguishes between two different types of traps. What Moldvay knew (but mostly failed to communicate) was that exactly one mechanic applies in any given situation, and which one applies depends entirely on whether the trap in question is a room trap or a treasure trap:
A room trap is a large architectural feature such as a concealed pit, or a block that falls from the ceiling when someone passes underneath. Indiana Jones movies are filled with of examples of this kind of trap. Room traps can sometimes be discovered by a thorough search of the area, taking great care and using common sense. Thus, any character who searches for them has a chance to find room traps. Dwarves, being most familiar with underground construction, have a 1 in 3 chance of finding them. All other classes, including thieves, have a 1 in 6 chance. The thieves' ability Find or Remove Traps does not apply to room traps.
A treasure trap is a devious little mechanism such as a poisoned needle hidden in a lock, or a vial of sleeping gas which shatters when a chest is opened. These kinds of traps are intricate and cunning. Only thieves possess the special knowledge and training needed to uncover treasure traps and disarm them. This expertise is reflected in the thieves' ability Find or Remove Traps. Only thieves are able to find or remove treasure traps without the aid of magic.
Note: The terms room trap and treasure trap are Moldvay's, which he coined on page B52. I find them a little misleading, but I have kept with them for the sake of consistency.
RATIONALE
There are many passages in the text which support the notion that Moldvay saw a distinction between the kinds of traps that any adventurer can find and the kind that thieves alone can find and remove. Equally important, there are no passages which contradict the notion.
- Page B22, in the section titled Traps
Dungeons often contain traps, such as a trap door in the floor which springs open when a character walks over it...
All the examples of traps given in this section fit the description of large room traps, and it says these are the kinds traps to which the 1d6 mechanic applies.
- Page B9
They [dwarves] are expert miners and are able to find slanting passages, traps, shifting walls, and new construction one-third of the time (a roll of 1 or 2 on 1d6) when looking for them.
The references to mining, passages, construction, and so forth make it clear that by "traps" here he means large room traps not small mechanisms. The 1d6 mechanic is employed in this case, as expected.
- Page B10
They [thieves] are the only characters who can open locks and find traps without using magic to do so.
On the surface, this statement seems to contradict the rule that any character has at least a 1 in 6 chance of finding traps. However, Moldvay is referring specifically to the thieves' ability to find treasure traps and so there is no contradiction. Thieves really are the only ones who can find those.
- Page B10
A thief's training includes learning how to pick pockets, climb steep surfaces, move silently, hide in shadows, open locks (with a set of lockpicks or burglar's tools), remove small traps (such as poisoned needles), and how to hear noises better than other humans.
Here he is going through each of the seven standard "Thieves' Abilities". When he comes to traps, he only mentions removing "small traps" and even gives an example of just what he means by that.
- Page B19
It also takes a turn for a character to search a 10'x10' area, for a thief to check an item for traps, to rest or to load a bag with treasure.
Note that he gives the specific example of a thief checking an item for traps, and this activity is treated as distinct from searching an area.
- Page B52
A Trap may be located in an empty room or on treasure.
Moldvay calls these two types of traps "room traps" and "treasure traps" and lists some examples of each. At this point in the rules he is describing a system for randomly stocking dungeon rooms. It could be a coincidence that he took this either-or approach. On the other hand, this seems like just the approach he would take if he felt it important that a DM who runs a randomly stocked dungeon should know the type of each trap in order to know which mechanic applies to it.
- Pages B55-B56
The example of populating Room 3 has the DM determining that the room should contain treasure with a trap. Further down the page, the final description of Room #3 has this:
The safe is trapped with sleep gas which will billow out unless the trap is deactivated.
This indeed sounds like a treasure trap and so only a thief should be able to do anything about it. The fact that he says it can be deactivated (without explaining how) suggests that he's assuming a thief would use his Remove Traps ability.
- Page B59
Silverleaf is checking for secret doors, Fred is looking for traps, Black Dougal is examining the box, and Sister Rebecca is guarding the door.
I believe that here Moldvay is giving us an example of a party using the different trap mechanics to best effect. Fred (Fredrik) is a dwarf and with his 1 in 3 chance is the one best suited to search for room traps. Black Dougal is a thief and the only one suited to search for treasure traps.
It later notes that the DM rolls for Dougal's "Find or Remove Traps" ability while he examines the box. According to the "Thieves' Abilities" table, being 2nd level gives him a 15% chance of success. The 1 in 6 room trap mechanic would have given him a 16.6% chance of success, if it applied. Certainly Dougal would insist that the DM use the mechanic which has the greatest chance to succeed. But the fictional DM didn't use the 1d6 mechanic, the reason being that he couldn't. Dougal is examining an item for traps, not an area, so only the thief ability applies.
- Page B21, in the section on LISTENING
LISTENING: A character may try to listen at a door to hear what is on the other side. For each character listening, the DM should roll 1d6. A result of 1 (1 or 2 for demi-humans) means that the character hears any noises being made by the creatures on the other side of the door (if any). [...] Thieves have special chances to "hear noise" (see page B8).
Although this one does not relate directly to traps, it does show us how Moldvay handled a situation where he saw an overlap between a thieves' ability and something any class can do.
Any class can listen at doors, and the mechanic for this uses 1d6. Thieves have their own chance of success which improves as they go up in level. But unlike other thieves' abilities which use d%, Hear Noise uses 1d6. Moldvay saw an overlap between the thieves' ability and the general one and so he unified the mechanics.
The fact that Moldvay did not similarly unify the mechanics for finding traps lends further support to the notion that he didn't see any overlap between the thieves' ability and the general one.