Science is and will always be our best shot at being correct about the universe, but it's performed by imperfect humans. There's very little we can know for certain, so we have to pick our poison - either trust strangers who claim to have done their research, or trust our own fallible instincts.
I don't think there's a single correct answer to that question, but don't pretend like you're not choosing a poison. These "I believe in science" mantras are no more scientific than any other attitude.