Hmm...here's my thinking about it.
First, this isn't something where all the arguments are on one side. There's no explicit statement anywhere that I've seen that says, "for all intents and purposes, shields are a type of armor." There are only places that refer to lists including shields as lists of armor, and other places that refer to armor and shields, as if they're two separate things.
So we have two recourses:
1) The intent of the game designers, figuring that they spent years balancing this game, and that if we follow their intent, our own games will be similarly balanced; and
2) Logic.
Logically, a monk gets cool wisdom bonuses to armor because she's dodging blows. At least, that's how I see it. Armor and shield relies on a different tactic for avoiding damage: you interpose a solid object between yourself and your enemy, and let the enemy hit that object.
I can easily see ruling that monks who make use of a shield's armor bonus cannot simultaneously make use of their Wisdom dodge bonus, in the same way that a barbarian can't rage and fight with expertise simultaneously.
As for a monk's other abilities, I'm not sure. In my own game, I'll go with the designer's intentions, though: unless I have a good reason to do otherwise, I stay with their interpretations of the rules. And I have no good reason to do otherwise in this case.
Daniel