I have always been amazed by faith in statistics. The research community itself shakes in awe before the totems of statistics. One of its most powerful idols is the 5% level of significance. I never knew how it could access such a level of universality, but I can I venture a hypothesis. The first statistical tests, such as Student's t test were compiled in statistical tables that gave reference values for only a few levels of significance, typically 0.05, 0.01 and 0.001. This gave huge leverage to editors and especially peer-reviewers (famous for their abusive comments) to reject a scientific work on the ground that it is not even substantiated by the weakest level of significance available. The generation of scientists persecuted for showing p-values equal to 0.06 learned this bitter lesson, and taught it back when they came to the position of reviewer. It then took very little to transform a social punishment into the established truth that 0.06 is simply not significant.
And frankly, I think it was a good thing to enforce a minimum level of statistical reliability. The part I disagree with is the converse statement...