quantum electrodynamics - Why isn't light scattered through transparency?

I'm asking a question that has bothered me for years and years. First of all, let me give some context. I'm a layman in physics (college educated, math major). I've read Feynman's QED cover to cover, and watched his messenger lectures. My hope is to get an answer at the "Feynman level", ideally in the crystal clear terms that feynman himself uses :)

Okay, so with that out of the way, my question is about transparency. My understanding from Feynman and other materials is that when a photon hits an atom, the photon can either be absorbed, or absorbed and released.

What I don't understand is how transparency could arise from this. If the light were absorbed and then a new photon emitted, it seems incredible that the new photon would have the exact trajectory as the old one. Why wouldn't it go off randomly in a random direction?

Here's some of the homework I've done trying to find out the answer on my own:

1) Transparency of materials (one commentor alludes to scattering not being explained here)

2) http://alemassociates.com/mambo/content/view/33/1/ (this seems to address it, but I will admit it's mostly over my head)

3) http://www.av8n.com/physics/white.htm (seems to talk about it, but doesn't explain why the photon would ever come out the same direction as it came in)

4) Discover magazine posted this: "when a packet of light energy, or photon, hits a solid object, three things can happen. Light can disappear: If the photon has the same vibrational frequency as the electrons in the material it strikes, those electrons absorb its energy, changing the photon from light into heat. Light can also be scattered: the surface electrons can grab the photon's energy and then eject a photon of the same wavelength which is how you see pretty much everything that doesn't emit light on its own. But if the photon doesn't have the right vibrational energy for absorption, and if the atoms in the material are arranged in patterns that discourage reflection (such as the random jumble of molecules in glass or air) then the photon's energy passes from atom to atom, emerging on the other side still bright and shiny. Then you have transparency."

I'm posting here for help. I realize that this forum is geared for graduate level and beyond physics, but I'm hoping that this transgression will be forgiven. I would really, truly, like to understand why anything is transparent at all. From my understanding, nothing should ever be transparent! At best we might get translucency (a bunch of photons coming out in random directions), but I cannot understand transparency. Why would a photon interacting with an atom come out the exact way it came from? In other words, as per that Discover magazine article, why would the photon be passed from atom to atom always at the exact same vector that it came from?

Thank you!

edit: If possible, I'd like to keep it in terms of photons. What's going on at the photon level, and avoid the wave framework. Let's talk about photons and probability amplitudes a-la Feynman.