Mecanim: undesired mesh intersections

I am using a 3D-model that I bought on-line and rigged it in Cinema4D. In Unity3D I want to use Mecanim for the animations. I tried using animations from "Mecanim Locomotion Starter Kit v1.3" and also from "Raw Mocap data for Mecanim v1.1", both for free in the asset-store.

Problem is that the arms are moving through the body. I assumed Mecanim took care of avoiding unwanted mesh intersections, but probably I am wrong. Does anyone have tips for me on how to avoid these mesh intersections?

This is before the mesh intersection:

![alt text][1] [1]: /storage/temp/10339-model+before+mesh+intersection.png

And here the arm goes through the body: ![alt text][2] [2]: /storage/temp/10340-model+with+mesh+intersection.png