I think you are greatly underestimating the impact of two things: one, the explanation based on science is often subtle and also often requires a significant amount of intuition for probabilities and statistics; and yet, two, there are people out there who loudly yell easy answers that prey on our biases.

My point: I find it difficult to talk about "earned trust" when not also acknowledging that the truth is often confusing yet boring, and there are people who actively espouse a simple, exciting, yet false alternative.