Not really. I’ve been the co-owner of a car dealership for 10 years and I never publicly talk about my “ownership” or allow people to brand me as such. Nor do I ever refer to my crew as “employees”...it’s always “coworkers” or “associates”.
Furthermore, to assert that the term “owner” and, by extension, “owned” is innocuous is laughable. It carries a lot a weight in the terms of a business arrangement. Any business owner can and should echo my position.