That's not actually how Thieves in AD&D or for that matter AD&D exploration works. You just described exactly what I said happened all the time - the DM defined some way that the PCs could be undetected when the rules didn't actually support it.
Normally, you're moving quietly, you could be heard at up to 30' away. If you were in metal armor, 90'. A Thief's ability was to potentially not be heard at all and with extremely poor odds of success.
i.e. DMs defined a set of house rules allowing for 'smart exploration' and then players did it. Or in some cases, the players had to figure out what the rules were and death would happen until they did.
OK, as a guy who ran 1e and then 2e during their entire times as the principle versions of D&D, so 20+ years, I don't know of this 'rule' that you are citing. I went back to the 1e PHB and the 1e DMG out of curiosity, and indeed no such statement exists in either one. Its entirely up to the DM what 'making noise' means. DMG p62, under surprise, Distance: paragraph 2
Noise:. It just states that if one party is "making considerable noise" then the other party can either flee or conceal itself (no mechanics given for this, presumably it hinges on there being some viable concealment).
In general AD&D doesn't have specific hard and fast rules for silent movement, noise, and concealment. Thieves have specific rules, but if you peruse them they're meant to apply to extraordinary situations. Moving Silently for instance is described as the ability to move quietly
even across a a squeaky wooden floor. Hiding in Shadows means being able to remain observed
by remaining motionless when in sight. No one can normally remain unobserved when in sight, but a thief can. No one can normally cross a squeaky wooden floor, but a thief can. Normal people can't Pick Pockets AT ALL, but a thief can. This is all less explicit than in OD&D, but still true, and quite clearly was the intent when the thief rules were created.
So, it was assumed that adventurers were competent and they could sneak around, as long as they were sneaking around on hard floors in the dark and making sure to be quiet and out of sight. A thief could actually hide in line of sight of a bad guy, though he still needed SOME sort of 'shadows' to do this (IE he can't stand next to you and be invisible with this skill) and he couldn't HIDE while you were watching. Likewise he could move over broken glass and not make noise, with some luck.
Of course what you have to understand is that the monsters have the same basic competencies. A bunch of goblins can quite literally walk up to the edge of the party's torch light and WILL NOT be detected, assuming no measures were taken (and this is why spells like Alarm are so useful). In that case the DM will apply the factors in the section on surprise and encounter distance to determine exactly how close the goblins actually get (or the party if its going the other way). DMG 62 provides the rules for this, encounter distance will be d6+4 inches (IE 50 to 100 feet). If one group is surprised, then the distance becomes 10-30 feet (1-3 inches). Assuming a party with torches and some goblins then the goblins cannot be surprised, they can see the party's torch light. The party can't see them unless they are within 4" (the limit of torch light). This means the goblins could get surprise, the party cannot. Assuming they do, then the encounter will start at 40 feet, otherwise at 50 to 100 feet or the limit of terrain (IE it can't be more than the available distance in the location where the encounter happens basically). Presumably at that point the goblins announce their presence in some way, and then each side rolls for initiative.
You can see how in this system scouting is quite effective, and while a thief is going to have somewhat of an edge on this in some sense, he's not actually grossly better at it than anyone else. Anyone can advance quietly under favorable circumstances. A ranger is actually the best, as they have bonuses related to surprise, though elves have a similar ability (its not clear that an elf ranger has any added advantage here, but I don't think there's any way in 1e to actually be a PC elf ranger).
The upshot of this is the DM has a couple of 'levers' to use to decide just how effective the party can be in a given situation in terms of scouting and otherwise maintaining control of the situation, but they do generally have the ability to do so, gated by the prevalence of infravision amongst monsters, which tends to make it tougher. Still, unless the DM is really trying to be a dick and thwart all attempts at skilled play, the players should have a pretty good chance of avoiding melees, but they will still get into some. Hirelings are the next line of defense of course. A wall of light infantry at the front of the party is fairly cheap and USUALLY means that the PCs can survive most of the crazy ganktastic encounters.