Is there any way to explain this?
The rig for this model was not really designed to look good in Blender—it was probably created in Maya or something. This is what's creating the strange appearance. You have a few options:
1) Delete the rig and create your own from scratch. Just hit X to delete the rig.
2) Manually fix every single bone to look good. (This will take extensive time and effort for potentially little reward.)
3) Deal with it. Just play around with it a little until you figure out the rhyme and reason behind the rig. Get used to it, and then use it all you like.