Look, the obvious truth is: D&D is whatever it's publisher publishes.
This is wrong. They can publish what they name D&D, but they have no ability whatsoever to determine what D&D is to me. There have been 5 different editions, as well as BECMI that have all been different. And those are only the 5 so far. There were be more versions of D&D, plus all the different D&Ds that we the players have made.
Every edition of D&D, EVERY SINGLE ONE, has been designed in such a way that it remains D&D despite all the changes DMs make to it. One of the design goals of D&D is for players to make the game their own version of D&D through changes, rulings, third party products, etc. D&D is designed to be changed and remain D&D.
If you want to play D&D like I do, as opposed to another game, part of the attraction is playing not a D&D game but the D&D game.
Just like they have no ability whatsoever to determine what D&D is to me, neither do you. You can't be right if you tell me that my altered version, and I house rule the crap out of every edition that I play, is another game. You can only tell me that it doesn't seem like D&D to YOU.
The exact line between "still D&D but with house rules" and "a different game" is, as you say, fuzzy. Or non-existent.
Non-existent. We each have our own individual lines and the company doesn't draw one. We can say what feels like D&D to us, but not what is or is not D&D for someone else.
What I do know is, that from my POV most if not all supposedly "D&D but better" games fail to remain D&D. They change too many things too much.
And that's fair. You get to determine what feels like D&D to you
I want a game that does not want to replace the PHB with its own "player's manual". It should change or replace a very defined set of things (see for instance the first post if this thread for such a list) and then not change or republish anything else.
Unfortunately, every edition or half edition like 5.5e does just that. There are significant changes in the upcoming PHB, DMG and MM. They also continually change rules as time goes on. See Tasha's, Xanathar's and other books that make modifications to the rules.
What you are asking for isn't something that D&D has ever been. TSR published changes to rules, additions to systems, etc. and so does WotC. WotC has also embraced 3rd party additions/changes to the game.