Admittedly, peer review originally referred to the fact that the journal being published was read ("reviewed") by your peers, and thus there would be the opport

Admittedly, peer review originally referred to the fact that the journal being published was read ("reviewed") by your peers, and thus there would be the opportunity for them to provide rebuttals after publication. The process the term now refers to in academia only emerged in the 50's and 60's (Nature for example wasn't "peer reviewed" until 1967). It was literally a marketing ploy to make journals sound more prestigious which got legitimized when certain grant agencies and regulatory bodies started including it in their requirements. All the best science is published in journals that describe themselves as peer reviewed, the government says science not published in such journals isn't up to snuff, and taken literally it seems useful. It's no wonder the public thinks it's an important and long established part of the scientific process.