"When you were there" is no contradiction to what I wrote.

I'm not going to try to argue what you saw at the tables you sat at.
Out of curiosity, seeing as you were there, can you think of any written references from 1974 or 1975 to rolling under an ability score as a common method of resolution? Snarf and I and a few others had a big discussion about this a while back. As we all know, the first time TSR described it as an option for a general resolution method was in 1981 Basic. I have no doubt that the concept was older, but I've often been curious about documentation for that. The 1978 Players Handbook has one or two similar special cases, the closest being the Dig spell describing how someone avoids falling into a pit, but the language used* implies that this is an unusual procedure, something they don't expect the readers to already be familiar with. Describing it as a kind of saving throw rather than the now-standard terminology of "ability check" which we've all been used to for decades now, and which I think made its first appearance in a TSR product in the glossary of the 1989 Players Handbook.
*"Any creature at the edge (1’) of such a pit uses its dexterity score as a saving throw to avoid falling into the hole, with a score equal to or less than the dexterity meaning that a fall was avoided."
Bearing in mind that people were inventing it as they went, and it didn't become common to apply the term "roleplaying" to describe it until a year or two later, as publishers struggled to figure out a better term for these games than "Rules for fantastic medieval wargames campaigns".
We all know there was no "persuasion skill", but of course one of the few mechanics which did exist was the reaction roll (p12, Men & Magic), which laid out how to roll dice (adjusted for Charisma) to determine, for example, whether an NPC could be talked into serving or helping the PCs.
5E always had and currently still does have a similar idea as a rule. Don't roll unless there is both a meaningful chance of success or failure, AND a meaningful consequence for failure. The PH mentions this right in the first paragraphs of the rules for checks (p10), and the DMG breaks it down in more detail for the DM on page 27.
That's a bit of an overstatement about 3E. While 3E did over-mechanize for my tastes, it also includes the rules for Taking 10 and Taking 20 to eliminate unnecessary checks.
A bit much to answer all your questions, but to answer off the start, the rules were pretty vague (if you've ever taken a look at them, you could realize that). A lot was passed by word of mouth or what was passed on from what was seen at other tables...etc.
As I said, the two main ways were roleplaying it out or rolling under ability scores. That's just how it was. You can choose to decide that you want to plug your ears, but that's what was going on. I have no idea that it ever referred to rolling under your ability scores as a type of resolution in the rules (so, you stating it was in 1981 rules is actually news to me, it may be but it's probably something I glossed over or forgot about). If it was in later rules, it was probably because it was already a common type of resolution already.
However, the roleplaying I'm talking about was actually extremely common for anything out of combat (and for some groups, combat as well. The first group I ever played D&D with didn't even use dice for combat, it was completely DM fiat). You can see it in articles about Dave's orginal table, you can see it if there are any videos of Gary's old gaming table. This idea that roleplaying it out was something modern is ridiculous. The reason they probably didn't include a lot of the out of combat resolution ideas was because it was accepted that this was just how they played and everyone else would play (which actually pertained to a lot of what was or was not in the original rules. Things that were accepted as just simply...logical...on how one would play something wasn't even thought of to write it out in some ways...though obviously it was not so logical or obvious to everyone, and certainly not to many).
It's hard to explain how it was back then. DM fiat was actually a majority of the game. The DM would be the one to decide things. However, there were those who had task resolutions by rolling under ability scores as well. A combination of those would not be odd either. (Edit: and I just want to add, because of this form of explaining what you do, the game itself was a lot more free in what people chose to do in many instances. It's one of those things i just can't really explain, but it was a lot more free. People literally could choose to do anything or be anything if they wanted, without as many constraints as you see in rpg's today. I'm sure there are tables which may still do this, but I haven't seen them myself in a very long time. It was like...there are rules...but at the same time...there is a lot of freedom and you do what you really want to try to do).
The more modern day type of Roleplaying I think came about because people didn't like that style of play. How does one roleplay a charismatic character? How does one roleplay sneaking around while swimming in a pool? How does one...etc...etc...etc. People didn't want to talk about what they were doing and explain it, they'd rather just roll (from what I can tell). Originally, I think Gary was actually sort of opposed to the Thief, and he was the one I think that added the percentiles to it. However, that didn't really change the style of what was going on or how things were played overall.
That all started to change though as people started wanting something more specific, rules that were more organized and rules that could be used at tournaments (which require a more standard numbers approach than a talking approach). The origiinal game was sort of like two games when it was first played. It was very much a wargame in which you had individual characters, but it was also a very narrative game outside of the areas defined by a wargamer's approach.
The closest I think I could compare would be the original Warhammer 40K Rogue Trader game which also had a RPG rules which you could play, but the rules mostly pertained to the combat portion with the actual outside of exploration and combat being left more freeform and up to the GM to decide what to do. Or a more modern example would be sort of like Gloomhaven which has defined rules for the boardgame, but beyond that with no rules it's either the text of the scenario or if they want to expand beyond that, their own imaginations.
PS: I should add much of this is anecdotal...or from my personal experience. I did not have access to things such as ENworld, there were no massive studies done, all my experiences were from what I saw was happening on the gaming scene and other locations as a teen (not a full adult yet, even). Granted, the bunch playing D&D was a lot fewer and a much smaller group back then, but I obviously didn't see everyone who played the game. I saw enough around the Indiana, the midwest, and later the UK (more around the 80s era for that, and it was more akin to how you'd expect 80s D&D to be played at that point) to appropriate the common ways many were playing in those areas...but I will grant that they could have been playing some other way in California, or Utah, or out West, or in Canada...etc.).