I think like he said, it is all trust. Without trust, people are wary of your motivations. When you are in that position, having the people you don't trust do things like promote the narrative of "trust science" just looks like they are using scientists as mouthpieces to co-opt their trust to push a narrative. Moderating misinformation looks like censorship, mandates look like coercion, etc.

Overall it was just a colossal failure of communication by policy makers, who had already eroded most of their trust before the pandemic, which then got exacerbated by contemporary journalism that felt like it had no qualms about making everything as divisive as possible for engagement.

I don't think people have lost trust in science, but politicians using "science" in this way of communication are doing a pretty good job of trying to erode that trust.