Yeah, and in the case of Zapdos and Moltres, this is despite technically meeting them the first time in Island of the Giant Pokémon and right before the Indigo League, respectively, well before Pokémon 2000.
Heck, even the anime can't get its own episodes straight, like how the Brandon rematch infamously had wrong flashbacks to the Kanto team, or how May claimed she had previously used Skitty in a previous contest when she had actually used Beautifly.
As far as the movies' canonicity, we most certainly know that Movies 1, 2, 7, 9, and most likely the DP trilogy at least are canon, since Movie 1 was heavily alluded to in various episodes (and even got a sequel of sorts with Mewtwo Returns), Movie 2, as noted above, was referenced in the Whirl Islands arc, even in the Japanese version, Movie 7, let's face it, when the home town of a certain rival is explicitly a movie-only location, there's no denial that it is canon, Movie 9 had the Manaphy in that film being referenced in one of the episodes, and so far as the DP trilogy, for starters, Dawn had that lunar wing she got in the episode where Darkrai appears, which she only got in Movie 10, and since the succeeding two movies were part of a trilogy instead of being relatively stand-alone, that by extension makes Movie 11 and 12 canon as well. In fact, I'd argue ALL of the movies are canon anyhow. Probably the only ones that MIGHT not be canon are those Pikachu movies, though even that's in the gray area.