The principle involved would not be breed or type specific.
You can't be serious. You actually think that a jury would draw the same conclusions about a chihuahua "attack" that they would about a pit bull attack?
If you have a guy shooting people with a .22, you have a problem. If you have a dog running around biting people, you have a problem.
If you have dogs fighting dogs, I frankly don't care. If you don't like it, control your dog, and control access to where your dog is. Hide your precious little pet in your house (as I do my cats) lest the big bad world scare you.
The good news: keeping your dog in the house gives you a reason to subscribe to the NY Times, or the LA "Dogtrainer". That will cushion the freefall of those two corporations.
The principle, if it exists,
involves property rights, responsibility and accountability,
in the case of an owner allowing their dog to free roam
and that dog being attacked by an another owner's dogs on that owner's property
In all the cases of this type there is an attack and injury.
The severity of the attack while relevant to the costs of vet care
is irrelevant to the question of who should pay.
The question is, who is responsible for paying the vet bills?
The person whose dogs do not leave his property during the incident
or the owner who let their dog run loose?
It appears you assume there is one principle for "pit bulls" owners
and another for all other owners.
God forbid I should ever let my Amstaff roam free
and he was attacked by "pit bulls" on someone else's property.
The contortions our principles would have to undergo would make them appear like pretzels.