Given your prior knowledge you should be skeptical, but given his experience James Miller should also continue to do this training. It's seems low cost - no more stressful for Alex than other activities that parents often force their children to partake in and with a potential very large payoff.

Also, James and Alex are going much further than the constraints of what a study can realistically expect of people. To use an analogy. Suppose you did a study on whether a bench press can increase muscle mass. Suppose you didn't know that bodybuilders exist. Suppose you ran the study for 2 months, with twice per week bench press sessions. Even with a very large sample size, do you think your results would have supported the possibility of extreme body building? I doubt it. It's very hard to push the average person to the level of training needed to see substantial gains. But it doesn't tell us what is possible.