I was giving a very general comment on what the p value tells you as I understand it. I am not enough of an expert in the theory of statistics to understand the distinctions you are raising The way I interpret a p value of a test is that you either reject the null or you don't - and if you do not it means that you can not be sure that the effect size you found was not due to random error in your sample. That is it would not exist in the population.