While there are valid criticisms of the way statistics are sometimes misused in science, pretty much every one of them comes from lack of understanding about how statistical models work - scientists reaching for a familiar test and following a formula they were taught. I can't blame them too much - understanding the true purpose and nature of statistical models is HARD (my recommended step one: become a Bayesian). What we need is for more people to recognise when they don't have that understanding and work with somebody who does.
What Briggs seems to have done, though, is decided that because HE doesn't understand statistical inference and modelling, that statistics are bunk. Taking a simplistic definition of "trend" like "the second-half average is higher than the first" and turning that into a boolean yes/no answer is the statistical equivalent of being an anti-vaccer.
The most frustrating thing, though, is that all the alternative definitions of "trend" he defines can actually be expressed as statistical models! The issue is that when you express these definitions/tests for "trend" as models, you see that the statements each model makes about the underlying system are very problematic.
TL;DR - Briggs doesn't understand statistical modelling, and has therefore concluded that his home-rolled tests are just as good.