When you say TRUE NATURE are you talking about dogs like some bully breeds which have deep dog aggression? I think those dogs cannot change to any degree.
What about plain straight dominant dogs--those that are tolerant towards dogs that won't challenge them in any way? I think these are hard cases because the dominance often carries over to humans as well as other dogs. Foxx is unique in that he is dominant towards other dogs & people but has a ton of pack drive which I had to learn to tap into.
Then the learned aggressor--the dog that has learned that aggression results in the dog getting what he wants--whether the dog had a bad experience with another dog while young, frustration, possessiveness etc. I think these are the only dogs that can be helped to any extent. Although after the first aggressive incident, there's always more of a chance bites will occur again. These are the dogs Jack helps because Jack is so confident & happy, he doesn't even care.
E-Dog - 2012 WPBTCA National Championships
The time when screech owls and Bandogges howl and spirits walk and ghosts break up their graves.
Act I, Scene IV of William Shakespeare's "King Henry VI"