All very neat, Fred, but I fear the truth is probably far more prosaic. The relationship started when wild carnivores, including doggie relations, started to hang around human dwellings feeding on the discarded remains of animal carcasses. The animals had better teeth than humans for stripping the last remnants of meat from the bone. The humans would have tolerated this as it kept the hungry animals from getting too close and it also cleared away remains which could otherwise have festered and caused disease.   Today, we see scavenging dogs and foxes in an entirely different light, but in those times there were no weekly collections, tin cans or plastic dustbins. The point is that the humans were already useful hunters, making up in guile what they lacked in pace.   The kind of small prey that dogs could catch would not have been of much interest to the humans. Few birds were available for dogs to catch (no guns huh?) and there were no rabbits (and probably no hares) as these were introduced much later.

And dogs have pretty rotten eyesight.