Wasn't the origin of PM "let's add Melee physics to Brawl?" The core PM team was originally modders from Brawl Plus if I'm not mistaken.
I want to preface this by saying that I really don't have much of an opinion either way about Project M. So, I'm honestly doing my best here as someone who really isn't a pro Smash insider to assess this in as nuanced a fashion as I can. I play more Smash 4 than anything just because it's new and the easiest thing to play online, but I promise that I'm not advocating for or against any particular faction of the Smash community.
With that out of the way, I don't think this really rebuts the claim as strongly as you think. Mind you, there's room for interpretation here, but I think modding can aim to achieve any of several different goals. I'll break them down into 3 categories in a haphazard fashion:
1.) Enhance or tweak non-core aspects of the experience. These are things like adding higher resolutions, better textures, more aspect ratios and so on. This might also include UI tweaks where applicable, or unlocking more options in the menu to allow for more flexibility to the existing rules in the menu. Except for things that might affect multiplayer balance, I think these are mostly harmless from a developer perspective.
2.) Take the existing game and throw it completely out the window to make something completely different. By this, I mean something like take the Smash engine and turn it into a pure platformer or something else completely different that isn't a fighting game. You know, just show off what the engine can do by expanding the playground. Like 1 above, I think these are mostly harmless from a developer perspective.
3.) Change the core gameplay. Sometimes, this might involve benevolent bug fixes and be a welcome change by a team that just doesn't have the resources or infrastructure to officially fix the old thing. But I think there is room to interpret this as a challenge to the intended design when not tweaking something that is objectively broken. And I don't mean "objectively broken" in the "some fans don't like it" sense, but in the "actually does not work as intended" sense.
So when you ask: "Wasn't the origin of PM 'let's add Melee physics to Brawl?'", I don't think that gets around the idea of how it can be seen as an affront to the intended design of Brawl. Yes, I think it can be seen in a flattering light that a dedicated group of people wants to put in the time and effort to make a game play like something that you've previously made, but if you're someone that is proud of Brawl and proud of Smash 4 and sees these iterations as improvements on the past work, it's not surprising that a group of people looking to undo those new intended changes can be regarded as a slap in the face.
I don't think this is an easy thing to address. I'm not saying that Nintendo shouldn't try, but I don't know if it's easy to please everyone here. Whether it ultimately succeeds or fails in the long term, I think in the short term Nintendo HAS to focus on Smash 4 as much as possible. After a certain amount of time has passed, they might be able to evaluate the next move forward, but I think they're kind of stuck right now having to push 4 as the future of the series. They certainly can't acknowledge Project M, and I don't think they can/should try to kill off Melee, but I also don't know what their options are to please the tournament community.
Long term, I think there are some interesting considerations that probably won't happen anyway. One is to make the Melee HD game the Melee fans want so much. The other would be to resuscitate a dying Smash 4 community (if and when it happens) by officially supporting some sort of Project M-like DLC for Smash 4. You know, try to iterate on Smash the same way Capcom does with Street Fighter. I don't think this'll ever happen, but even at an optimistic level, I think we're a good year away from anything like this being planned. For now, I don't think there's really anything Nintendo can do but try and focus on Smash 4 as THE Smash game.
I'm distracted with work and I kind of feel like I'm rambling and not really making a point, so I'll just stop here.