This is something that seems to get missed in the public rumination of "trusting science" — because no one likes nuance, and few people actually understand what scientific reasoning really is, those that do understand it have to justify their pragmatic faith in other scientists to the contradictory hyper-skepticism of conspiracy nuts, while cautioning those with an uneducated devotion to anything loosely labeled "science" to be a little more skeptical, while also countering the misguided purists who like to claim that (as you said) anyone can conduct science in their basement and that here is some straight-and-narrow path to scientific truth.

We have to stop teaching science as a bunch of facts and only getting to what science really is — a way of reasoning — when the student has already figured that out enough to want to pursue it at a doctorate level, while everyone just thinks it has something to do with dinosaurs electron and if the word "science" is contained in the sentence somewhere then it must be true.