Disclaimer: I am not familiar with the DWA law verbiage. I am speaking about people owning 'dangerous animals' in general.
Personally, I don't believe most people should own exotics to begin with [again, I am speaking from a personal standpoint, not a legal one]. Most people are not even equipped to give parrots or reptiles the care they need.
Whatever animal someone owns, welfare and quality of life has to be first priority. Dog, Cat, Goldfish - all animals. I've seen too many cases of people owning 'dangerous animals' and the animal's welfare, as well as the safety of their family and neighbors, is jeopardized by the ignorance of the owner (e.g. Charla Nash, Terry Thompson, Cynthia Lee Gamble, Jason Coats, etc). Sure, maybe it can be done right, but I don't believe this is the case for most private persons, especially with Chimpanzees and big cats.
The difference between private persons and rehabs/sanctuaries possesing wild animals is clear. Their stay in these facilities is of single purpose: medical treatment or refuge due to seizure/surrender from someone who provided inadequate care. Their stay with private persons? Because someone wanted one.