This seems like a really long winded way of explaining the p value.

My understanding is that it is a measure of the confidence that the result is not down to pure chance. A p value of 0.05 suggests that there is 5% likelihood that the result was down to chance, rather than the intervention. 0.05 has been set as the threshold of acceptable risk that the result is trustworthy. It does not mean the result is 100% accurate.