Take nobody's word for it – evidence and authority in a world of propaganda
However, if everybody’s word has to be continually checked by everyone before it is accepted, things get very slow. Generally there is an accepted body of knowledge, published in respected places in enough detail that further repeated experiments probably aren’t needed, and new experiments can be designed to build upon the old. We don’t check J.J.Thomson’s 1897 discovery of the electron any more; we use electrons to do new experiments.
My own experiment, ATLAS at the CERN Large Hadron Collider, is a horrendously complex piece of technology relying on the cumulative knowledge of more than a century of science, and the hard work and ingenuity of thousands of people; engineers and physicists, but also accountants, project managers and more. We check and double-check things often, whenever we can. But over and again we have to trust each other, take each others word for key facts. Otherwise the collaboration simply would not function.
Both science, and the society that sustains and is enriched by it, are too complex for everything to be checked from first principles by everyone personally before they act on it. Some things have to be taken on trust, and this is where authority creeps back in, of necessity. If someone, or some organisation, has a track record of accuracy and honesty, they are more likely to be believed in the future. We also weigh up how much attention to pay to their claims by considering how well they fit with what is already known, the ‘seamless web’ of overdetermined knowledge.
When that trust is undermined, the first thing is loss of efficiency, and the next is a total breakdown.
This is why no one with the best interests of science, or society, at heart can afford to openly lie, whatever side of an argument might appear to benefit in the short term. Acknowledging uncertainties is vital, owning up to mistakes deserves respect, and outright lies in the face of obvious facts mean the perpetrators must be cast out, and never listened to again. Otherwise they will break the whole system. Whether the system is science or democratic society, this may be their goal, and the threat must be resisted. Don’t just take my word for it.