I think that a way to look at the evidence from a different angle would be to look at what happens with athletes who don't believe in their training. Threads pop up on letsrun all the time "My coach is an idiot, what should I do?" Sometimes I read those things and think, "Yup, the coach is an idiot." And sometimes I read them and think, "This athlete just doesn't understand what the coach is trying to get out of certain workouts." Either way though, the athlete is probably underperforming. As a high school coach, most of the athletes who come into our program are new to the sport and so they will believe what I tell them if not because I am right, because they have nothing else to go on. We have a moderately active club group in our area though so we get a couple of kids every year who have run before. Many of our most talented athletes have come through these clubs. We have had great success stories and some disappointments as well that have come from the club athletes. I don't claim to be the perfect coach for all athletes or even a perfect coach for any athlete, but experience tells me that if I can convince an athlete that the work that we're doing is the best work that the athlete could be doing (even if I'm wrong), we get better results than if the athlete doubts the work. When that happens, the athletes either stop executing certain parts of the training with the necessary attention to detail (they get lazy and sloppy with parts), or they go to outside sources to supplement their training (an old coach, some local coach who thinks they are doing a good deed by giving every athlete from every team workouts based on their program, or something online). Some of the local club coaches and local coaches are pretty good and although not individual, there are great resources out there to learn about training. But when an athlete starts to mix and match things between my program and parts that they are finding in other places, that usually doesn't work very well. When an athlete believes in what he or she is doing, that doesn't really happen.
If the training plan is terrible, then belief cannot fix that, but I think that coaches who can produce an average level plan for their athletes and get the athletes to believe enough to execute it to their full ability, will ultimately have more success than a coach whose training plan is awesome down to the last detail, but the athletes don't believe in it and therefore, execute poorly.
I think the higher level an athlete gets to, the less that this matters. At each level, a higher percentage of athletes have decided to buy in to a very high degree. I think that it probably matters less in college than high school, but it still matters. At the professional level, it matters minimally, but it still matters.