Apparently only if they claim to be non-profit.
Scientists are not business people so it is easy to understand why anyone would confuse non-profit status with "doesn't make money". They all want to make money. So if one publisher can charge you $1,200 to buy out the copyright and another charges readers $150 to read science, who is superior?
It basically only depends on who you like.
But to the public it makes a difference. People who are getting something for nothing are going to take something; so an online newspaper, quality understanding or not, is going to get read by more people than a subscription-based journal. A pay-to-publish journal is also openly accessible to the public but someone is paying editor salaries so it's going to be libraries/subscribers or the public.
P.Z. Myers at Scienceblogs.com is discouraged by the somewhat lousy health reporting noted in a recent analysis but notes that the study itself can't be read without paying $25. It's delightful irony but what is the solution?
The solution is what I have long advocated; open publishing. In the modern world of Science 2.0 there is no reason at all Science should force people to buy a subscription or PLoS should force researchers to pay to publish a study. The Internet works. An advertising based mode clearly has had proof-of-concept for a decade and a half. BMC or PLoS or anyone else will contend it's right for them to claim costs in putting out a quality product but wrong for Nature to charge so much but that is just subjective. They charge what the market will bear. Editors at online sites, etc., will insist they work for too little, just like editors in print have always claimed. If we could charge readers $150 a year to read Science 2.0, we might do it, but it's more important to be read by the public, who otherwise are reading the tabloids Prof. Myers does not like, than to make money.
Bora Zikvokic is one of few with the experience of marketing PLoS first (pay-to-publish) and later a pay-to-read publication owned by Nature Publishing/The Macmillan Group/Georg von Holtzbrinck Publishing - seriously, that is how many layers of ownership Scientific American has - so he can see both sides pretty clearly, and his heart is likely with open access, but why?
If science results are for the public good, why not make them completely open? Free to publish, free to read. It works, we have 5 years of putting out great science writing and paying people to do so without a nickel taken from the government. A Science 2.0 model could make journal publishing profitable for scientists.
Additional: Another Scienceblogs contributor notes an additional bit of irony; he commented on Nature endorsing open blogs in a publication behind a pay wall and notes that Nature removed it as being spam. But Nature, at least Nature Networks, was always fundamentally flawed by heavy-handed management. I have(or had) an account over there and would ask general questions and before long a Nature editor would leave a comment pointing readers to an irrelevant blog by a Nature person. So it isn't something new.