Your mistake here is in saying that because the p-value is 1/32 you reject the null hypothesis. You just decided to do that with utterly no justification. There

Your mistake here is in saying that because the p-value is 1/32 you reject the null hypothesis. You just decided to do that with utterly no justification. There is a problem with people unthinkingly deciding that a p-value of .05 is reasonable is most situations but that is not actually an issue with frequentist statistics anymore then people starting out with bizarre priors would be a problem with Bayesian statistics.