Put the whole issue of the paper mills aside for a minute. Here's how a normal process works:
The author(s) of a study send it in to a relevant journal in the relevant field.
The study is then perused by the journal editor or assistants (some of whom may be graduate students!) to determine possible peer reviewers. Generally speaking, the journal editor will be unpaid, or have a small stipend, but their main job is as a professor in some institution. The graduate students may be doing this job to get out of teaching or lab work as part of their own arrangements with their institutions.
Once the editor has picked from their stable of possible reviewers, they basically query whether the reviewers are available and willing.
Mind you, the reviewers are themselves usually professors who - and this is important - receive almost no benefit whatsoever for conducting the peer reviews. No pay. No stipend. Nothing.
(OK, OK, I can hear the objection: reviewing is part of their job as a professor, so they do get paid. To this, I say hogwash. The incentive structure for professors put "reviewing for an academic journal or publisher" at the absolute bottom of the accomplishment scale. Nobody gets a merit raise for number of reviewed manuscripts.)
So, the reviewers are there toiling away for free. Sometimes they do good work. Sometimes they phone it in. To do good work on some scientific papers requires a great deal of care and competence. To do good work in other fields requires a great deal of built up knowledge and discernment.
Then the paper is sent back to the editor with the verdict: publish, reject, or revise and resubmit. The editor passes that on to the submitting author(s), and the cycle starts again.
I want to emphasize that this process is insane. If peer review is broken, it's not merely because these ethically deficient numbskulls are flooding the journals with fake papers, but because the whole thing is built for a nineteenth century academic structure. It's a dumb system even if it were working correctly.
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