I read your definition of a beta reader vs. an editor with a good deal of interest:
The first link you provided above,Ten Tips to be a Better Beta Reader by Corrine Jackson), has a slightly different take on the function of a beta reader:
My own experience helping several authors with their work is that they define the responsibilities of editors and beta readers differently. The assistance I provide includes all the functions these definitions cover. I make suggestions about the story line, the characters, and improvements in wording. I would never overlook a spelling or grammar error. So, which am I? I don't think it matters. As long as an author has several people reviewing his work, there's a good chance all bases will be covered.
Most important, I think, is that everyone realize that producing a story requires teamwork and the author is the team leader. The final decisions are always his. I don't get upset if the author declines to use my suggestions.