Loosely-speaking, I see your point and understand what you're saying.
Strictly-speaking, if Hollingsworth didn't make the breeding, then it's not a Hollingsworth dog. In fact, Hollingsworth not only didn't breed the dog himself, but he didn't breed either parent, nor even 3 out of 4 of his grandparents. (He did, however, breed 5 out of 8 of your dogs great-grandparents.)
When speaking of dog breedings, my own viewpoint for proper terminology would be a choice between two ways of seeing this pedigree: 1) who actually did the breeding or 2) the dog blood irrespective of human names.
If we choose 1, then Southern Kennels bred your dog, he bred his parents, and he bred 2 out of 4 of his grandparents (actually owning 4 out of 4 of the grandparents). SK's influence and breeding choices are much greater and much more direct on your dog than anyone else's.
If we choose, 2, then your new stud is a triple-bred Mayday dog, with extra helpings of Dolly and Polly on the bottom, and an extra helping of Yellow/Deadlift on top
Jack