Depends on what is meant by "running the show".
If by that it means who controls hiring coaches and so forth, yes of course Jerry "runs the show". He's the owner, it's HIS team. But that would mean that the citizens of Green Bay "runs the show", as the Packers are a publicly owned company, but what does even a major stockholder in the Packers have to do with hiring coaches, drafting players, etc.? Absolutely nothing. So, you have to consider other things as "running the show".
Such as the actual evaluation and management and using the players to actually play the game. And in that regard, obviously Jimmy "ran" the team.
Otherwise, it would mean that a man who spent 25 years in the oil business was able to build a multiple Super Bowl championship team in 4 years, and a coach who had spent 25 years coaching football had less to do with that.
Which of course makes no sense, building an NFL team isn't something somebody can just drop out of the sky and do. It's a skill, and like most any skill it takes practice and experience to be really good at it, and winning Super Bowls takes immense skill.
But really the whole thing is so silly, everybody who follows the NFL knows full well that that Jerry Jones bought the team, hired Johnson (and he probably could have hired any number of other NFL coaches to run the team, not saying he didn't recognize something in Jimmy that gave him the idea Jimmy could get Jerry's team to the top of the heap) and if nothing else learned the NFL game so that he could recognize talent, etc.
There's room for both men on the podium of the Dallas Cowboys success from 1989-1993, sad Jerry can't see that....
