There are many things I dislike about your former employer.
However, the quoted passage is probably one of the best techniques I've run across in a crew environment. We adopted the format at the former employer. I resisted at first, but after the first line use of it, loved it.
There were many things I disliked about my former employer but the training dept was light years ahead of some of the training depts I came in contact with. (sorry if that offends.. after Continental I think we were one of the first to adopt grading
up mistakes that were caught and handled without consequence instead of belaboring the debrief listing all the mistakes without noting the correct actions <monitoring, challenge, response, etc )
The Capt running the checklist actually came out of a NASA study and used first at a regional. One of our Check Airmen read about the program, noticed that during Emergency Descents when the F/O was flying there was often confusion over who did what. The pressurization panel was right in the F/Os face and s/he was used to using it.. for the Capt, it could be tough with glasses and at night. Somethings were often missed and who grabbed the speedbrake. So.. the first change was to make the ED procedures
seat specific and the first action was Capt flies. Yes, I know this is not a Capt runs the checklist situation. But it was the beginning of looking at who did what and where the final authority lay and who did what.
Instead of interrupting the Capt flying with the F/O doing "Bloviation Valve Selector Normal/Shutoff" and the Capt being distracted, it boiled down to after the bold actions (which we did away most of), it was, "You have the airplane.. we are at 220kts, clean, level at 3500.. you have the radios, Advise ATC... I have the checklist..." and the Capt would advise the F/O of each decision. It worked like a charm and in no time at all, everyone jumped on it.
Now retired from airline ops and back to Gen-Av I have seen that in some, if not many cases, that has yet to trickle down and many checklists are still read/do. (even the normals) and some are still calling out Normal and Expected stuff on engine start (Valve open.. N2... oil pressure.. N1 etc). Fortunately we don't at my new house and we only call when things are unexpected or abnormal... er.. 'non-normal' to use the jargon.