This is a pretty bad paper. It shouldn't be taken too seriously, as indicated by the no-name journal it's published in, but I'm bored so I'll give some lengthy comments:

On one hand, since the “randomization” test in the context of a randomized clinical trial is an example of a permutation test, much of the argument in favor of randomization as an experimental principle has been that there is a guaranteed correct statistical test. This argument has had an enormous impact on the design of biomedical studies, with virtually all researchers agreed that randomization is necessary for a study to be valid. If a randomization test is invalid, however, then the technical argument for randomization becomes rather thin.

No, the major argument for randomization is that it guarantees that the expected effect of any unobserved factor is zero. If you don't randomize then unobserved factor effects may have non-zero expected values, which completely fucks up your inference. There's nothing thin about the argument for randomization, whatever the status of permutation/randomization tests. This guy has a PhD in biostats, he should know this shit.

Now let us look at the situation with different eyes. Suppose that Figure 1(a) shows the distribution of