I think this is like the difference between homeopathy and medicine. If you're sick and go to a doctor, you have a chance that the doctor will find a way to cure you. If you're sick and go to a homeopath, there's no chance that the homeopath will find a way to cure you. Similarly, peer review has a chance to catch errors before they make it to print, while absence of peer review has no such chance.

Peer review is not infallible, neither is it a mark of scientific quality, as you say. I appreciate that people tend to use it like that- you read, in articles in the lay press, that such-and-such study was "not published in a peer-reviewed journal" as if to say that we can't be sure of the quality of the study and that, conversely, if it was peer-reviewed, we could. That's not right. Peer review is not a sufficient condition to guarantee correct results. It's not even a necessary condition. Like I say in my comment above it is one mechanism of modern research practices that helps improve the quality of published papers.