They do not own the Open Source trademark. They tried to trademark "open source", but the USPTO denied the application. Since then, they've worked at convincing the public that OSS means anything with a license approved by the OSI. This too is not so. For example, SQLite, arguably the most successful OSS tool ever built, is not covered by an OSI license and doesn't intend to be.
SQLite has been dedicated to the public domain, ostensibly removing all copyright restrictions. Technically, it has no license for the OSI to list as an OSI license.
