Yes; it is another one of those Ash/Red ideas. While one is based on the other (in this case Ash being based on Red), they are NOT the same character and to say/assume that they are is incorrect. Therein lies the discussion; the separation between what is Anime and what is Game.
Ergo, the in-game Mewtwo is NOT the same character seen in the anime. As can be seen and has been discussed about here previously, the backstories of the two, while similar, are not exactly the same. In-game Mewtwo was 'born', with Mew having given birth to it (note that this was written/made before the idea of Breeding and Eggs were introduced). The baby was christened Mew-two, though became vicious. they tried to 'curb it's vicious tendencies' but failed.
As a result of that, we can assume that the Cinnibar Mansion was originally a lab of some sort, or secretly housed a lab within it, and was destroyed when Mewtwo was unable to be restrained, and he then fled to the Cerulean Cave to be away from humans and/or to be surrounded by other strong Pokémon. I believe there is also some speculation as to whether Mr. Fugi owned/was the scientist who studied Mewtwo, and also may have some connection with the sign on Faraway Island, and in turn the Emerald event.
Again, I reiterate, the Anime was based on the games, and NOT the other way around. To assume the two Mewtwo are the same is incorrect. However, if mewtwo is to be in HG/SS, does anybody else think it may have anything to do with the Berserk Gene that one could find outside of where the cave once was in the originals?
