Well, most reviewers aren't even paid in closed access journals. The thing that is wrong with scientific publications is the following:
The researcher needs to be published in journals with a certain reputation IF she wants to remain researcher and climb the latter in an academic career. So she has a clear incentive to publish even for free, even for some amount (if it is a book), because overall more she has published, more chances she has to stay in academia.
The universities are attracting research funding (public or private) as well as students with strong spending through reputation. One of the simplest measures of reputation and the most pertaining to funding are published articles per faculty, department, etc. So they have a strong incentive to further raise the incentives of their researchers to publish in journals - no matter how they are funded. And indeed, requirements of publication per year have become a common part of the job.
Reviewers usually don't touch that much money - the incentive again is here the need of reputation to attract funds and/or advance in academic career. Reviewing is just part of the game.
Most academia then needs to stay in touch with current research, so besides going to conferences, they need access to journals. So there is also a guaranteed buyer base.
So now we have the conditions why publishers have the possibility to retrieve so much money (because the research come in for free and most editorial stuff is outsourced without equivalent to the researcher and reviewers) out of the system and why they have an interest in pursuing the strictest possible copyright application possible. I have read some estimates that a big academic publishing house has a margin of 37±2%.
The case of JSTOR and Swartz is a little different. JSTOR is not a publisher but a platform, that facilitates the access to online content, working on a non-profit base. Their move against Swartz seems to have been mostly precautionary, so that their job will not be hampered through due diligence suits, etc. As far as I know, both parties agreed.
In case of public/private research, access varies hugely across subject. In social sciences the more private the research the more it is free. In some natural sciences general access is mostly assured for free (but without the review part). In turn, private research is rarely published in those subjects (except for the patent files). The whole discussion is therefore not so easily solved by the public/private argument, but rather how to assure good quality research (f.e. through a continued review process and incentive to make use of it) and affordable access at least to the most interested parts (students, libraries and users). Open Access seems to me the best option, as most participants are already working "for free", which allows these huge margins of publishers. Except for this tricky problem called reputation (or "grading"). Another way could be to limit the copyrights on articles to 2 years or so. This would lift the load on many mid-class universities and small scale research institutions as well provide some compensation to the "evaluators" for their work. In consequence, much money could be saved at institutional level that could be reinvested into more research (or grants, etc.), while preserving up to date research access.