Parts of computer science are not too bad either. In my field, AI, the top-tier journals and conferences are all open-access and run by nonprofits. I mention conferences because in computer science they are important as well; the top peer-reviewed conference proceedings are as important as journals.
* The top two journals are probably JMLR (machine learning) and JAIR (AI in general), both open access and run by nonprofits. No publication charges either.
* The top two general AI conferences are AAAI and IJCAI; the top two machine learning conference are ICML and NIPS. All four of these publish open-access proceedings (including archives of past proceedings) and are run by nonprofits.
Of course this didn't happen entirely by default, it's taken some effort over the years. AAAI has always been nonprofit, but its digital library has not always been open access. And in machine learning, the top journals used to be run by the Elsevier/Springer duopoly, which was solved in the early 2000s by 40 editors of Machine Learning journal, which included a large proportion of top researchers in the field, resigning en masse to start an open-access alternative: http://www.jmlr.org/statement.html