There is no "Save or Die" mechanic in OD&D or AD&D.
|Not the DM's Fault|
This is a classic situation in the fantasy that forms the roots of the game - the villain casts a dire spell and is astounded as the hero resists it; or the supposed poison only incapacitates the victim or is shrugged off.
Saving throws and hit points represent that particular type of author's favour that allows the central characters to get out of "impossible" scrapes or survive against massive odds. As the characters rise in level they become more and more central and gain more favour. Thus, there is no direct connection between a character's ability scores and their saves (other than some flat bonuses) - Frodo saves well because he's important in a metagame sense rather than by dint of high ability scores or other in-game reasons.
The phrase "Save or Die" is really part of the mythos of the legendary Killer DM (much spoke of; seldom encountered) in early gaming fostered by those who have "contemporary design sensibilities". The two go together because a DM who wants to can arbitrarily declare anything a "sudden death" situation - falling down the stairs; eating mushrooms; climbing a wall. S/he can put poisonous snakes in the beds of the inn or giant spiders in the PC's coach. Of course s/he can!
The fact that AD&D doesn't have a rule that says they shouldn't doesn't change the fact that the players can up and leave because the DM is a moron. There's no rule against being a killer DM but there's no rule to say that anyone has to put up with it either.
But the problem with putting rules in to control such a DM is that you end up with rules that limit all DMs while the bad ones will just find other ways to be annoying (there's an infinite supply).
The saving throw mechanic is part of a players' ability to make a judgement - if I do this I have a chance to make it. The alternatives should be obvious and top of the list is "run away" or at least "don't do that". The player knows that the touch of a ghoul paralyses or that a medusa's gaze will turn them to stone or that a room full of gigantic cobwebs might mean poisonous spiders and that might mean poisonous bites. It only becomes "Save or Die" when the DM (and not the player) eliminates the choice of facing the danger.
Of course, the players don't know what's around the corner much of the time but that's just another way of saying "we're not scouting very well". Whether you're in a "funhouse" dungeon or a more logically balanced scenario the party that allows their fate to be determined by random rolls without trying to minimise the number of those crucial rolls is responsible for throwing away the charatcers, not the DM. Calling the act of repeatedly and blindly putting your head in the lion's mouth "save or die" is to put the cause and effect the wrong way around.
Later editions of the game gradually moved away from true exploring towards a bland conveyor belt of combat. The game system took on responsibility for producing encounters which the character party could face with a set level of danger. The players no longer had to worry about making sure that they were not walking into a deathtrap - instead, deathtraps were made illegal. Ultimately we end up with fourth edition which is simply a sort of chess on steroids battle system, with even the roleplaying reduced to a bunch of dice rolls in the "Skill Challenge" system. I'm not sure where the "challenge" is in that, unless it's to avoid RSI from the dice rolling.
It's a testament to the standards of players out there today that this attempt has failed both strategically (the game was a flop) and tactically (many players who do play 4e have hacked this sort of rubbish out of it). Players - yes, even youngsters of the "entitlement generation" as many Grognards refer to them - actually don't want their minotaur delivered in a box for free XP, even the ones that like tactical skirmish games. Which is probably a good thing for imaginative DM's everywhere who want to invent actual challenges for their players to try overcoming; there still is an audience for that sort of play.