For what it's worth, I do think the Ameraucana site is incorrect that hatchery EEs are mutts. Araucanas were developed FROM hatchery EEs that a few people really liked the look of better than any of the other EEs that were floating around, and they managed to get an extremely consistent bird within what would be an impossibly short amount of time if they were working with mutts.
Several of the hatcheries - Meyer and Murray McMurray are two I am aware of - got their breeding start (or whoever they contract their EE eggs from got their breeding start) from the quechua fowl that were brought up to North America in the first half of the 1900s. Meyer says (I have a good friend who had this exact conversation with them) that they do NOT mix their EEs with anything else, that ALL of their EEs lay green eggs, and that they are all dark/partridge colors.
That makes their EEs pretty dang close to what we'd call a purebred - since there are no closed stud books and no pedigrees in chickens, visual is all you get. If they reliably pass along a body type, comb, color, shank, and egg, that's all we ask any poultry purebreds to do.
There are also hatcheries, and individuals, who define any mutt with chipmunky colors as EEs, no matter if they have the right comb, shank, egg color, body type, or anything else. Those kind of assertions muddy the waters for everybody else and give rise to the idea that every EE is a mutt. EEs are actually quite valuable to a whole bunch of breeding programs, and their eggs are commercially valuable for the same reasons that Marans eggs are (novelty of color equals higher demand). So I think it's a bad idea to say that every EE is a mutt and every mutt is an EE.
Down in my brooder I have seven Ameraucana mixes (dad was a blue Ameraucana, moms were EEs). They hatched from blue eggs, not green. Every single one has feathered in solid blue or solid black, they have slate (not willow) legs, they have pea combs and nice leg separation. I have plans for the pullets among them, but I'm not going to call them EITHER Ameraucanas OR EEs when they're grown. They're too "improved" for me to be comfortable calling them EEs and they're not going to breed true to color and so cannot be Ameraucanas. They're headed for my Leghorn roosters to create a terminal cross of heavy-laying blue eggers, which will ALSO be muffed/bearded and pea-combed but will be neither EEs nor Ameraucanas. I have too much respect for what EEs are and have been (and could be) to call any cross an EE.