Why do we trust in mathematical proofs? Answer: because one (theoretically) doesn't have to trust authorities, but can check the proof oneself. The same holds for results from empirical sciences: They can be falsified and lots of experiments have been done with the intention to falsify the theories and failed.
By the way: This is also a strong argument for open access (because parking scientific results behind paywalls makes this really hard).
Thus science is not about trusting authorities, but about being to verify yourself (structural sciences) and all. In other words: Science is about distrusting authorities and verifying/falsifying yourself.