The editorial team could be selected through a semi-democratic process, if required.
Is it that tough? How many big names in science are required to pull this through? The technology is dead-simple - the main problem is to cross the critical threshold of number of articles submitted and number of editors.
The problem is that the system is broken - publish n papers => you're better than before (ignoring the content of the papers of course). Academics are encouraged to publish (and re-publish older stuff with a slight tweak) to meet publishing 'targets' handed down by government.
This model feeds into the Elsiver etc closed publishing as academics are forced to compete to earn their stripes - so now we have a model that encourages re-publishing crap and then locking it behind a paywall, but when I ask PhDs if they think this is fine, they don't see the problem :(
Are these journals explicitly named, or is there a criteria they need to satisfy to be eligible?
That company is explicitly not trying to do anything about evil publishing houses, but if it takes off, it will move one part of the publishing process out of the control of publishers, into the hands of scientists. If reviews through this system get to be known for high quality, then maybe a good review from them for your open-access paper will be more prestigious than getting it published in an Elsevier journal.