Legendaries

On the legendary pokémon page under 'Trivia' it states that "In all but one of the games, there appears to only be one of each legendary Pokémon..."

Is this referring to the Articuno in the GenI games which you can see in a pair of binoculars in the gate separating Fuchsia City from Route 15, or something else?

I believe it is in reference to the HeartGold & SoulSilver Arceus event. Despite notes of the original Dialga, Palkia, and Giratina existing & being created when Arceus created Sinnoh, Arceus is capable of creating an egg that hatches into a level 1 member of the creation trio for the player.

It's outdated then. Black and White had a Mystery Gift Victini as well as the Liberty Pass in-game Victini event. So you can legitimately have two Victini in those games without trading.

In general, a Mystery Gift like that would not be counted as it's an external event not directly coded into any of the games.