Quote from the anime:
That's plural ^
And so please give me some REAL evidence that says that there's only one and not just tell me two fansites that doesn't say that.
I couldn't find you alleged claim that there are more than one either. Only episode that refers to any of the three Legendary Birds with more than one in the Species was the Episode with Todd Snapp when they were in Johto where he mistakenly says "there are Articuno there" after hearing a story from Nurse Joy.
Though his wording hints, they never said that there were in fact more than one on that mountain. Every where else, there has only been One showing of the legendary birds.
The Episode when Ash tried to help a Zapdos recharge after spending all of its energy, a maiden says that Zapdos comes to the lake to recharge.
The Pokemon Chronicals Episode I refered to earlier, I mistook the names. The name of the Man trying to catch Moltres was named Silver and he had been following Moltres all around the world trying to catch it and noting each of its nesting spots.
Back to the Episode with Todd, the Nurse that tells them the Story says that Articuno had Nests all over the region and travels to them frequently.
Every Episode with Zapdos has shown Zapdos far away from the mountains as some would believe it would live showing the patterns of living areas for the two before.
In the Manga there were only one as well. Though since the Manga follows the Game's perspective, All Legendary Pokemon are supposed to be one of a kind. Even though the Battle Frontier Pyramid Brain uses the Golems.
So would you please show some real evidence to support your theory. Like maybe a Picture of more than one Articuno, Moltres, or Zapdos from the Anime or Manga. And not try to hide behind translated texts or hinted suggestions.