>>49082949There's a point where if you want an answer you have to accept that, by nature of being official and the only things that touch on the subject, supplementary materials are canon. Like how that old Red and Green pokedex had that stuff about nidorina becoming infertile and once that got translated people came to understand her and nidoqueen losing the ability to breed was intentional and not just a mistake in the database that never got corrected. Lugia was added to the games BECAUSE it was going to be in the movie, instead of just letting it be exclusive to the anime/movie universe like a bunch of forms of pokemon such as the crystal onix and that venusaur/blastoise fusion already were, in fact they probably could've stated it was just too important to the balance of nature to be caught or something and back then that would've been enough to stop the inevitable screeching when little Timmy couldn't actually find the cool pokemon he saw in the theater since the hype started to die down shortly after and pokemania was completely dead by gen 3 at which point consistent lore started to become less important.
That being said, there is one game that explicitly links the birds to lugia. In Gale of Darkness not only does lugia get that recolor but it's Greevil/Cipher as a whole's big ace, so much so that you fight it alone with no other pokemon beside it or trainer commanding it, and it had an exclusive shadow move. Then you fight Greevil himself and he uses the birds each with their own unique shadow move as well, something none of the other shadow pokemon in the game got despite there being a lot more variety in shadow moves and pokemon in general than Colosseum had. They're the only obtainable legendaries and come in a set like how in Colosseum the admins had the beasts then let you get ho-oh if you prove yourself worthy. Those games had full battle and trade compatibility with main series, so it's at least a more direct connection than the movie.