As far as I can see, the skin only consists of one object: the PolyToSubDiv-object. This is the object I bind to the skeleton. I can't find any object in the Outliner which corresponds to the lowpoly-object in your description. Still, by looking at the picture it's quite obvious that I have two objects; one lowres-object which follows my skeleton, and one highres-object which "overreacts" to changes in the skeletons position.

Is there any way I could show both these objects in the Outliner, so that I can follow your advice and only bind the lowpoly-object?