I guess the moral is "Don't trust anyone but a mathematician"?

Safety in numbers? ;)

Perhaps it's useful to distinguish between the frontier of science vs. established science. One should expect the frontier to be rather shaky and full of disagreements, before the winning theories have had time to be thoroughly tested and become part of our scientific bedrock. There was a time after all when it was rational for a layperson to remain rather neutral with respect to Einstein's views on space and time. The heuristic of "is this science established / uncontroversial amongst experts?" is perhaps so boring we forget it, but it's one of the most useful ones we have.