I've always taken "public ownership" to imply "publicly-traded company", which means John Q. Public can call up his broker and buy some shares in the company.

This in contrast to privately-held companies, which can and do have many owners, but whose owners are acquired through partnership, investment, key employees within the company, and M&A - but not through the sale of securities.

Does that mean you oppose all companies or business which are owned by more than a single person?

No that's still private ownership. Amazon, for example, is not collectively owned, even though it's owned by more than just Jeff Bezos.