They literally say in the first sentence that they will run a public instance on Mozilla.Social. This means they will own that instance.

You could argue that no one owns anything exclusively in today's federalized world but that is not true in practical terms. They will own the identities/social graphs/content created locally. "Own" meaning they have total control over that instance and can, for example, enforce Mozilla-friendly policies, remove content, ban users (without the ability to export one's identity and social graph).