The peer review process is certainly a very large component to creating trust, but it's not just the process that's in place at the moment, it's the past track

The peer review process is certainly a very large component to creating trust, but it's not just the process that's in place at the moment, it's the past track record and reliability. An untrustworthy source cannot instantly turn into a trustworthy one by adding quality peer review, it needs to develop a track record, which takes time. Wikipedia is a perfect example. It has only relatively recently become seen to be trustworthy, after many of years of tweaking and improving their edit process. When Wikipedia first started, few took it seriously. Likewise, when an open journal starts adding more stringent publication requirements, it too will not be immediately trusted. The point is that quality itself is not sufficient. You need a reliable level of quality over a relatively longer period of time.