So this is his defence of what he phrases as the worst position, but what’s the minimalist position? He uses a vibrating collar to force his dog to stay on a bed while he streams?

This is completely disconnected from what he says and what we have any evidence for. The point of vibrating collars isn’t to torture the animal, but to give them a fast and unambiguous signal at any distance that you have conditioned them to associate with a particular command or set of commands (e.g. “come to your owner,” “pay attention to your owner,” “stop being aggressive”). Kaya is left off-leash outside a lot and it’s reasonable to have something like a vibration collar for communicating in a fast and unambiguous manner with your dog over distance. It’s not “this thing is shaking and it will continue to overstimulate you until you submit” it’s basically just like a vibrating phone or something acting as an alert by momentarily providing a stimulus.

He has Kaya stay on the bed most of the time when there happens to not be other people in the house to watch her out of concern for her joints. She’ll be off-camera somewhere else in the house for long stretches of time when there are other people around to watch her.

he can surely afford carpet

He has carpets, but the floor is still harder than what is ideal for a big dog to sleep on. You’ll notice that she has a suspension bed for this reason.