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.

In their view, yes, if you don't conform to their prescriptivist take on the subject.

The fact that they have fooled so many people into thinking they own a trademark on a generic phrase is, however, pretty impressive.