Perhaps the Ho-Oh given to the player is not given, per se, but rather, it joins the player of its own free will, since it is in search of a pure-hearted Trainer. But for some reason or another, it does not consider the player to be its original Trainer, thus explaining why it "belongs" to Mt. Battle. Also because of this, Ho-Oh must move on at some point, so perhaps Wes releases it, whereupon it flies to Navel Rock.
The Lugia caught in Pokémon XD was caught for the sole purpose of purifying it. Therefore, it is reasonable to assume that Michael released it upon purification, and it fled to Navel Rock afterward.
The Rainbow and Silver Wings supposedly summon Lugia and Ho-Oh to their respective nests in G/S/C/HG/SS. The Wings do not simply allow passage. Therefore, it is reasonable to assume that the birds were summoned from Navel Rock.
