To be clear, we're talking here about the general category of "things stated by scientists", not the more specific "things stated by scientists about the findings of the scientific process." Many people conflate the both of these as "trusting science" — and that's a problem.

You can believe in scientists' claims about what scientific studies say/mean, or about what the scientific consensus on a question is — without believing any random claim a group of scientists makes about any random subject.

Specifically, there is strong reason to treat scientists as just like any other group of people, where claims about how the work of science gets done (e.g. whether it's possible for a lab to have an accident resulting in a leak) are concerned.

You suggest a terrible alternative. Much better would be "believe nothing".

It is terrible, but it is what we are looking at.

It would be naive to believe that every single person out there is equipped with the knowledge and the critical thinking skills to discern between good and bad information, thus it would be vastly preferable that people trust science.

This is called a strawman