Sorry about not responding for awhile, got rather tied up with something.
Anyway, I'm using 3ds Max 2013 with the latest product update which is 6 I think. They don't seem to have barely any service packs at least by name so yeah. This is the version that the bug is being tested on... but I don't think it's actually Max's fault. It's Hammer.
While this may not be a good lead, I notice that when I turn on collision model visibility in Hammer, it tints it a different color depending on what prop it is. For static, it's red and for physics it's purple. As you seen from the screenshots, it's a physics prop with the collision tinted red.
What I think Hammer is doing is trying to treat it as a static prop when it isn't and tosses out all except the collision hull skinned to the root bone. This also occurs with a dynamic prop that has animation on it but the animation is perfectly fine. It is the collision hulls it is apparently tossing out.

I probably have to blow Hammer away and reinstall it to see if that solves the issue. If that don't work, I'll put the models in using another game such as Counter Strike and then open the map up in the game I'm mapping for.
Again, the model and collision appears perfectly fine in both the stand-alone model viewer and Hammer's model browser. When it is put into the level is where the problem appears to start. There may not be anything you can do in this regard so... yeah. I'll let you know if that fixes it.