Animator on sub-node of fbx file does not work?

I did something similar to the Unity Stealth game example for opening and closing doors ( http://unity3d.com/learn/tutorials/projects/stealth/single-doors ), except that I had my door in the same scene file as the level, including the animations, exported to the same .fbx file.

Everything appeared to be fine when I set up animations using an Animator Controller for opening and closing the door, the state transition previews looked great, but when I ran the game the animations did not play at all.

I found out that if I placed my Animator on the root node from the fbx file instead of on a subnode (the door), the animations played as they should! But if the Animator is on a sub node of the fbx file it came from, then it does not play at all.

Anyone else had any problems with this? I would like to be able to have the Animators on sub nodes without exporting multiple fbx files. How do I do that? This seems like a bug to me..

(If you try the Stealth tutorial for sliding-doors, mentioned above, and just place the Animator on "door_generic_slide_panel" instead of on its parent "door_generic_slide" then that demo won't work anymore either)