Blender to Unity faulty Skinned Mesh Renderer.

I am creating assets for a cell phone game, and have characters that are made of individual meshes parented to armature joints in blender. I did this to avoid using skinned mesh renderer and use normal mesh renderers instead.

Unfortunately, Unity disregards the hierarchy and applies a skinned mesh renderer to EACH mesh parented to a joint when I drag the file into Unity. This is the exact opposite of what I had intended.

There are no armature modifiers or vertex weights in the .blend file. Any ideas on how to stop Unity from trying to rig my characters?