I know the studios don't consider it canon...
I'm amazed that this myth persists. It hasn't been true for over two decades.
What happened was that in 1989, Gene Roddenberry issued a memo which basically declared that the animated series wasn't part of the canon. That was his
personal preference, and it was binding as long as he was the one running the show. But then, in 1991, Roddenberry died, and his preference for how to treat TAS ceased to be binding the moment that happened. There have been a number of references to ideas from TAS in subsequent canon, as early as "Unification" referencing the events of "Yesteryear."
True, there are a few TAS episodes that have been contradicted by later works, like "The Magicks of Megas-tu" and "The Slaver Weapon." But then, there are live-action movies and films that have also been contradicted. The way "The Alternative Factor" portrayed antimatter and dilithium has been contradicted by all subsequent and prior
references to those substances. VGR: "Threshold" has been officially declared apocryphal by its own writers. VGR: "Fury" made claims about the difficulty of changing course at warp which, again, all prior and subsequent Trek has contradicted. And the ease of travel to the center of the galaxy in both
"Megas-tu" and The Final Frontier
has been contradicted by DS9 and VGR. Any long-running canon ignores or contradicts earlier parts of itself eventually.
Not to mention that TAS is fully included on Memory Alpha as part of the canon material rather than as apocrypha, and it's counted on Startrek.com along with the other series and films. And nobody's kept the tie-in novels, comics, and computer games from referencing TAS for a long time now; indeed, such references have only been getting more frequent in the past few years.
So the studio doesn't treat TAS any differently than it treats any other Trek series. And really, it's not the studio's place to say anyway. They don't care from canon, they just want to make money. It's the current creators of new screen material who define what counts and what doesn't. That's why Roddenberry's opinion was law so long as he was the showrunner, and why it stopped applying when he died and his successors started working in TAS nods here and there. As for the current creators of screen material, they practically remade scenes from "Yesteryear" in the first act of the 2009 movie, so that makes their stance pretty clear.