Yes, there are certainly many different types of "madness". The "layer of abstraction" that the specific variety of madness imparts on the holder is their own reality. The hypothetical accepted objective true reality is irrelevant to them. While this true reality is the standard with which to measure the conduct of people's behavior, if you are to preserve the emotional well being of the suffer of madness it would be helpful to communicate and act in a way which is consistent with their own subjective reality. By delving into their madness you can understand their behavior and actions more than understanding it from an outside perspective. If the goal is to simply enforce external standards this empathy is a waste of resources. But if preserving their emotional well being is a concern empathy can be a useful tool to both understand their perspective and guide you in your interactions with the sufferer.
http://www.youtube.com/watch?v=1Evwgu369Jw
At the very least I think it would have been nice if the hoarder in this story was taken away to alternate accommodations for the duration of the clean up. Terrible that she had to witness the event.