Completely. The short answer is that copyright law gives the copyright holder the right to make access open or restricted, and we seek to put copyright in the hands of authors or institutions that will consent to make access open. The long answer depends on whether we are talking about open access journals or open access repositories.
Open access journals will either let authors retain copyright or ask authors to transfer copyright to the publisher. In either case, the copyright holder will consent to open access for the published work. When the publisher holds the copyright, it will consent to open access directly. When authors hold the copyright, they will insure open access by signing a license to the publisher authorizing open access. Publishers of open access journals will have such licenses already prepared for authors. For more information see Report on the implementation of open content licenses in developing and transition countries.
Open access repositories. Authors of preprints hold the copyright to them and may post them to open access repositories with no copyright problems whatever. If the preprint is later accepted for publication in a journal that requires authors to transfer copyright to the publisher, then the journal may or may not give permission for the refereed postprint to be posted to an open access archive (SHERPA RoMEO site provides information about publisher copyright policies & self-archiving – use this site to find a summary of permissions that are normally given as part of each publisher's copyright transfer agreement). If permission is granted, then again there is no copyright problem. If permission is denied, then the preprint may remain in the open access archive because it is a different work from the postprint and the author never transferred the copyright on the preprint. Moreover, the author may post to the archive a list of corrigenda, or differences between the preprint and postprint. This is not quite as convenient for readers as seeing the whole postprint online, but it provides them with the equivalent of the full text of the postprint and is infinitely more useful than no free access at all.
We do not advocate open access for copyrighted literature against the will of the copyright holder or in violation of copyright law. Nor do we advocate for any changes in copyright law. We seek to maximize access within existing copyright law, in accordance with the wishes of the copyright holders.
(Based on the Budapest Open Access Initiative: Frequently Asked Question)
For more information see (openoasis.org/index.php?option=com_content&view=article&id=152&Itemid=311) Author's Rights and Author Addenda in the OASIS and (openoasis.org/images/stories/file/Copyright%20and%20authors%27%20rights.pdf) Copyright and authorsʼ rights: A Briefing Paper [PDF] written by Kevin L. Smith, J.D. & David R. Hansen, J.D., Duke University for OASIS