I'd have two things to say about it. One is that I dislike any notion of alpha status that involves machismo and showy self-assertion. That's not how it is in the wild. I'd have sympathy with any trainer who emphasised a quite, non-confrontational concept of alpha status.
But secondly, and perhaps more important, is that dogs are all so different from one another, and so suit different methods. My current dog, a PRT, is very heirarchically minded, he really is. It makes training both vital and very effective. But my last dog, a Spinone, seemed blind to heirarchy. His breeding, I think, emphasised the communial, cooperative hunting behaviours of pack dogs, rather than the hierarchy of the pack. He was a little sod to train, but when he was sniffing after pheasants he always looked to me and responded to my behaviour closely, because in his mind we were hunting together.
So I'd say, alpha status is important but perhaps not the only natural influence on dogs' trainability.
I'd be suspicious of a trainer who said 'no' to alpha-establishing methods, but with the relevant kind of dog I would welcome someone who had more than this one string to her bow.
(And you mention positive reinforcement as an alternative. Positive reinforcement is clearly vital and central, but not an alternative to the alpha-seeking appproach? They are complementary I guess??