You'll need to prove that.
I'm running 1e and I don't like lower female racial stat caps, so I need to change the rule. Can I do that? If not, show me the page and quote that says I can't do that. If I can, then I can literally change rules as I see fit. All I have to do is say I need to do it and declare it so.
I mean, even if the books said you can't, nothing stops you. Nothing ever stopped anyone from playing any edition of D&D the way they wanted to.
As I pointed out upthread, the books really are written in a way that assumes "of course you'll run the game using all the rules!", while only occasionally outright stating "this is an optional rule". I mean, you see that even to this day, with things like Encumbrance in the PHB- if all rules are optional, why bother labeling something as such?
1e in particular was written in a very ambiguous way when it came to telling people what they could do with the game. Again, as I stated above, we can only speculate as to the reasons. Was it Gary's ego? An attempt to drive a wedge between AD&D and the original D&D (plus the other games that were spawned in imitation)? A slam against third-party developers like Judge's Guild? Who knows!
At the end of the day, however, Gary often spoke out of both sides of his mouth. Finding a quote in a rulebook or Dragon Magazine, or elsewhere that supports one or the other side of this debate (and many, many others) is all too easy. And it doesn't matter what he or any of the other TSR staff wrote- I have never encountered two DM's games that were exactly the same. Even if they were bound to use the same rules without changing them (ala public play), their interpretations of the many many grey areas of the game made them distinct entities.
So why don't we just put this debate to rest? It's quite evident that most, if not all 1e products were considered to be essential by TSR at the time. This certainly fits "a" definition of "core", but not in the way WotC uses the term- ie, the minimum amount of books necessary to play the game.
2e is even worse- the Tome of Magic and The Book of Artifacts were seen as "core rulebooks", and all the DM and Player reference books as well. And over time, even things that were stated to be optional in the PHB, like Non-Weapon Proficiencies, were assumed to be the standard.
TSR never had a clear vision of "core rulebooks". Anything that expanded the game rules and helped you run and play games could be equally valid and considered "necessary". At no time did that matter- it's quite improbable to think every group owned every book- indeed, for many years, even having access to books could be problematic, if you didn't have a game store near you! When I started playing, I had the PHB, DMG, and the Monster Manual. I could check out the Wilderness and Dungeoneer's Survival Guides and the Fiend Folio from the Joliet Public Library.
There was no game store in the city (the "hobby store" catered to traditional hobbies like models, model trains, and Estes rockets). It wasn't until I moved to another community that I could regularly go to a hobby store (the long-extinct Castle Hobbies in Bradley) and even then, they didn't have
every book!
Would Gary say I wasn't playing AD&D? Who cares?