I follow the logic, but now you're dismounted, playing lion tamer in the middle of the road with a snarling dog. You still need to get out of the situation. Do you try to scare the dog off, look for a rock, hope he gets bored, hope he gets called in for supper?

In most cases, the dog, having nothing to chase and having made his point, gets bored and goes home . Most owners are also trying to get the dog called home or something . You may be in a rural area without leash laws, but that doesn't mean the dog can't be deemed a public hazard . You have a bike between you and the dog . Sometimes you just have to stall things with animals until they give up . Not all situations can be resolved without mace or pepper spray or waiting for someone to come along .

I try to ride with people that are slower than I am.

Yep, basically. I had an encounter with what I thought was a dog, but might have been a dog-coyote hybrid. He was kind of serious. When he got to within 15 feet of me, I squirted the water bottle at him. It fell well short of him, but he sat down on the spot. He kept barking and growling, but I started to walk away from him. Once I felt a safe distance away, I rode off. He never got out of the sitting position.

Well my point of view is running (riding) away triggers the dogs predator/prey instinct. 99% of dogs stop chasing me stop when I stop. They may or may not give up on biting me. When stuck in this position I just keep working my way slowly out of his "territory" while defending myself.

Of course if I can outrun the dog in the first place then I will. But I've seen some dogs run 35+ on the flats. Really most dogs just seem to be having fun. It's that 1% you got to worry about. As always YMMV so do what YOU think best in the situation.