MoonSong
Rules-lawyering drama queen but not a munchkin
You're missing the reason for this argument though. See, the HP=Meet crowd needs to show that the way they are doing things is the same as it's always been done and that 4e is the outlier. If they don't show that, then suddenly 4e's no longer the outlier and their interpretation is. If that's true, then there is no real need to support their interpretation, because their interpretation has never actually been supported. Their whole argument centers on the idea that 4e has radically changed the game and that they are simply trying to get back to the way it was before.
OTOH, when you actually look at the quotes in the rules, suddenly 4e is no longer the outlier. 3e healing rates were very fast, perhaps slightly slower than 4e, but, not by much. 1e and 2e interpreted HP as "mostly mojo" and rejected the idea that characters got "meatier" as they gained levels. Suddenly, their entire line of reasoning for criticising every aspect of HP is in question because, if HP are "mostly mojo" in every edition of D&D, then things like Damage on a Miss isn't such a huge leap, dealing damage with non-physical attacks becomes perfectly plausible, minions make a fair bit of sense, and healing rates similar to 3e or 4e aren't out of line at all.
So, it does hinge very strongly on what Gygax said. The whole argument hinges on reinterpreting HP to be something that they never were - mostly meat with a believable healing pace.
I'm sorry, but no. HP=Meat don't need to prove it was the one true way, all we need to say is that we didn't suddenly pop up into existence out of nowhere and that all other editions satisfy us.
4e is an outlier because it is the one edition that enforces one specific interpretation of HP while all others let you interpret it however you wanted. You say 4e healing rates don't vary from late 3.5, but I don't believe that is a fair comparison, in 4e full overnight healing is the baseline, while in 3.5 the baseline is one quarter of your wounds at most, only getting into super quick healing when assisted and using bed rest for a full day. That it is impossible to go faster than the 4e baseline is another thing entirely -and a reason it is less satisfactory to be the healer-.