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I'm sure your explanation is necessitated by events that happen later in the cycle, but I think it would have been more consistent with game mechanics to say that faith in Avacyn powers the magic but that as Avacyn's absense continues and rumors begin to spread about her disappearance, the faith of the people of Innistrad is wavering and their fear is mastering them and this is what's causing the failures in Avacynian protections. This way, it would still make sense for Avacynian magic to work on another plane when a planeswalker summons a faithful devotee of Avacyn or employs one of her artifacts; the strength of the belief of the wielder is what powers the spell or activates the artifact, no matter how far away in space or time Avacyn herself may be.
There's a weird interplay of invoked power, faith of the wielder, and the simple fact that white spells (and abilities) just seem to work. At some point, "it just works, even though it probably shouldn't" is at the heart of the notion of magic (little m), so we can't be too surprised when logic starts to break down. At the same time, there's no reason what's true in one case should be true in another. Mabe some white magic is based on invoking higher powers, some is based on the faith of the wielder, some is based on the strength of the convocation acting in unison, and some is based on interplay between them. All of those are consistent with what we know of white. There's nothing wrong with saying that there are no simple, immutable rules for this sort of things, aside from the fact it's not a particularly satisfying answer.
Edit: Also, I completely failed to notice this until I went back and looked at what Doug said again, but does it seem to any of you like he's confirming that Avacyn is just an archangel, even though a "mighty" one, and not a planeswalker? I'd always assumed that Avacyn was sort of a Serra figure, a planeswalker who got herself into a position to be worshipped as a goddess. However, it really seems like Doug is confirming that Avacyn is just an archangel and indirectly suggesting that her magic is weaker than Markov's. That might be reading far too much into what he said, though, especially if he's trying to dance around the big planeswalker reveal if Avacyn does end up coming back in Roll.