"Owner" is usually an overstatement. Yes, an activist investor has to own some chunk of the company (and it has to be a big enough chunk that management will pay attention to them), but they don't own the whole thing - or even a controlling interest. If they did, they wouldn't need to be activist, they'd just fire the existing board and management and hire people that would do what they want.

Instead, activist investors own a small, but large enough chunk, advocate for what they want and rely on other investors being passive (e.g. because a lot of the company is owned by tiny slivers of much larger portfolios) even if what they're advocating isn't in other investors' interests.