My understanding, based on my mere 24 years, is this:
The center of Christianity–and arguably religion–is “thy will be done.” We’re looking to achieve a harmony between the world above by mirroring it here. While I don’t have numerous examples in front of me, a few come to mind. For example, the layout of the Egyptian pyramids in relation to the Nile River apparently mirrors the layout of the stars in Orion’s belt in relation to the Milky Way. It’s celestial imitation. The Jewish Star of David is really the intersection of two triangles–a merger of heaven and earth. And in Christianity, it’s “thy will be done on Earth as it is in heaven.”
The point being–heaven gets it right; with all our problems, you think we’d be doing what they do.
Enter the paradox of free will. Yes, it’d be easier if God merely manipulated our wills or forced circumstances to achieve a desired outcome. It really would. But what would be the point? I say this not to make light of the little girl’s situation, but as I understand it, there’s a matter of human souls at stake here. We do not merely want to achieve a world that looks good, but is good. Hence, our free will exists as a matter of allowing us to love God–and each other–freely.
Why? Because something freely given is so much better than that which is forced. It feels better when a kid openly shares his toys with his younger sibling, rather than when the parent forces him to do so. In the latter case, your result is a pissed-off parent, one kid who resents sharing, and another who feels that the toy is an entitlement. In the former, there’s a spirit of love animating everyone. To force the issue defeats the purpose.
That means that everyone involved in our story 1) is a child of God, and 2) has free will. This includes the admitted jerkwad who kidnapped Elizabeth. I feel bad that he was driven by whatever circumstances–including his own greed and illness–to do this. (Caveat: I feel sorrier for his victims, so by no means am I advocating an excuse.) Regardless, I’d still argue that this character had the ability to love God and neighbor by not committing this crime. It’s possible that he wore down his own resistance to sin long ago–maybe he’s overindulged in kiddie porn to the point that he can’t say no anymore, beats me. The point being–and yes, I struggle with this too–is that God respects this individual’s free will by allowing him to make his choices.
God’s will, we can safely wager, was for Elizabeth not to be kidnapped. But his will was also for this guy not to do the kidnapping–we need to understand, it’s both of them at stake, and maybe from a larger perspective, Elizabeth’s parents as well. Prayer is the desire that God’s will be done–but as I’ve said, God’s will is not just a physical outcome (Elizabeth be saved) but also our participation in God’s will (the kidnapper quit doing this). Human idiocy, greed, stupidiy, or what-have-you, unfortunately, can get in the way of God’s will.
So, as I largely see it (and I realize I’m oversimplifying here): when good things happen, I’d ascribe it to God’s intervention. And let me make clear–when people help those good things happen–your police, fire, or woman with the cell phone–they’re participating in bringing about the good, so by all means, give them the credit. But when bad things happen–or more precisely, when people do bad things like kidnapping little girls–for better or worse, God can’t interfere with their choice.