This article seems very sensationalist and doesn't actually share many facts. You seem confused at best about what the terms you're using actually mean. Dominance ("alpha") theory and positive-only training are not opposites. They are both philosophies (and cults), but alpha implies a certain intention behind training. Dominance theory fanatics don't kick or shock their dog until it sits or lays down, that's just not how it works. Believing in dominance theory does not mean that you don't use positive methods. You can't get anywhere without incorporating some sort of motivation, especially when teaching commands. I'm by no means defending those who do believe in this theory, but you should be sharing the real reasons why dominance theory shouldn't be practiced -- specifically why it's flawed and discredited, with evidence.
Forget About Being Alpha in Your Pack -- Kathy Sdao, MA, CAAB
Dominance and Dog Training -- APDT
Comments on "Alpha" Dominance Theory by various people and institutions of authority
Depending on the dog, punishment isn't inherently abusive, and doesn't inherently fall under the category of dominance. Ignoring your dog when they act out for attention, removing yourself (or your dog) from a situation, withholding a treat when they misbehave, all leave the bounds of positive-only training. In fact, every time you tell your dog "no" you leave the bounds of positive-only training, as it is positive punishment (the addition of something to decrease the likelihood of behavior occurring again). Anything you do to decrease the likelihood of a behavior negates your "positive only" track record. You should make yourself familiar with the quadrant of positive/negative reinforcement/punishment (+P, -P, +R, -R) as well as the concept of balanced training. Dominance theory is merely a mindset and actually has little to do with training style.