Oops, the quote was from the article, not Feynman (I've edited my post now); note that the author is Gelman from 'the statistical crisis in science'.

But it throws back to Feynman's speeches on Cargo cult science, what is science and what isn't. The idea is basically the same, we can describe what good science is by the rigor put in the experimental process, but this is not something that can be captured simply by the p-value.