DOG BITE LIABILITY: Are there any exceptions to dog bite liability a California dog owner could use to escape legal liability (fault)?

Yes, there are narrow exceptions under California law.  The following circumstances could be used by a dog owner to escape legal liability (fault) if:

There is a possibility for the dog bite victim to enact or direct a legal claim to other (or against) possible defendants, including employers, landlords and dog breeders. It is even possible to make a claim against someone who negligently entrusted a dog to another person who could not control it, like a child. Claims against people other than the owner might be crucial under certain circumstances, such as when the dog owner lacks insurance.  However, to obtain legal liability of any other party you generally have to prove that the other party knew of the dangerous propensities of the dog, and where the dog was located (like for landlord dog bite negligence for instance).