@Benny: The bleed effect is a result of Desmonds prolonged exposure to the animus so the reason that Ezio can see Altair is not the same reason why Desmond sees Ezios memories without being in the animus. In short, the bleed effect is a side effect that just turns people crazy, or so the templars thought, but the assassins take advantage of this and trains Desmond with its help.
And it can't be the eagle vision(its inherited just like you said but its aluded to that other assassins also have that power since Subject 16 also had it, or S16 is related to Desmond) since that has never made them see something that isn't there, for example, a guy thats been dead for hundreads of years. Only POI and glitches/code/messages left by other assasssins.
I'll be interrested to so how they explaine why Ezio sees Altair since right now theres no way we can say for certain that one thing or another is the reason for that.
My random ass theory would be Desmond has spent so much time as Ezio, that Desmond is bleeding into Ezio in a similar manner, and so Desmond's visions of Altair are visible to Ezio. Considering the funky space lady at the end of AC2 directly addresses Desmond in the presence of Ezio, I don't think it's so far fetched to assume that if the Animus is based off their technology, such a thing might be possible.
I wanna say at the very least Ezio learns more of who Desmond is, he just kinda dropped the whole "Who the hell is Desmond?" thing in Brotherhood.
But when the funcky spcae lady talks to Desmond, it's in the past. That actually happened in Ezio's life, she wasn't talking to Desmond at that moment, but left a message for him to view 500 years later. Desmond suffering so much from the bleeding effect that Ezio begins to see Altair is impossible, because that means Desmond would have affected the past, which is impossible because the animus is not meant for time travel. If anything it's probably the seals (which devs have confirmed let EZIO live the memories of ALTIAR.) they're fundamentally an animus, just the primitive form, so my guess would be that from using those seals to see Altairs life, Ezio is getting his own bleeding affect.
I really think you guys are taking this too literally... I think it is just meant kind of as a metaphor because Ezio is following in Altair's footsteps and trying to find the secrets he left behind. He isn't actually "seeing" Altair.