I had one of those psychotic dogs. Got her when she was around 4mo. old. 3 vets and 4 behaviorists all agreed she had wires crossed. She was eventually put down because she thought biting people was the appropriate greeting. No amount of training was able to change that. It is rare, but it does happen.
I just read Cesar's Way (the Dog Whisperer book) and one of the most annoying things was his insistence on the potential to rehabilitate any dog. There are so many homeless dogs out there, how much effort is it worth to try to rehab an aggressor?