The naive public does not believe anything in particular about peer review. They think new scientific results are significant when they read about them in the popular media, that’s it.
People who do need to work professionally with peer review, do understand what it actually does and its limitations.
You seem stuck somewhere in the middle, caring deeply about a system you don’t seem to fully understand.
> The naive public does not believe anything in particular about peer review
You'd need to provide evidence or an argument for this. The media reports on things in part based on journal prestige, and likely when questioned, people will say they can trust such things because good scientists have looked at the work and say it is good. This would be an implicit belief that peer review is generally working well, even if they don't use the term "peer review".
> You seem stuck somewhere in the middle, caring deeply about a system you don’t seem to fully understand.
Extremely presumptuous, as I work in this system, and have provided plenty of evidence for my claims. You've provided only sneers.