The example you gave doesn’t make sense. First off you confused public trading (company shares are available to the general public) with public ownership (owned by the government i.e. “the public” at large). Johnson and Johnson is publicly traded but the shares are held by private entities. If I buy a share of Johnson and Johnson’s stock, I privately own a piece of Johnson and Johnson.
If a corporation is publicly traded, then its ownership is held by the public collective that chooses to invest. The ownership in question is not your specific ownership of a share individually, the ownership in question is the ownership of the means of production, which a public collective invested in. It is not true that you buying one share privately implies the whole thing is private. That’s like saying the fact that you voted in private means the government is privately controlled. Yes, private individuals can vote and buy stock, that does not make either private. It makes them public.
The definitions also agree with me btw
Private Ownership:
the fact of being owned by a private individual or organization, rather than by the state or a public body. (I googled “define private ownership”)
A public company is a company that has sold a portion of itself to the public via an initial public offering (IPO), meaning shareholders have a claim to part of the company’s assets and profits. (Same source)
ownership by the government of an asset, corporation, or industry. (I googled “define public ownership”)
So, if it’s owned by the government, or has shares available for purchase by any public body, then it is public. If it’s not owned by the state or public body, it’s private.
Johnson & Johnson, just like all public corporations, has its shares available for purchase for the public. Therefor, it is public, not private. Honestly, the more you go into it, the harder it is to get away from the simple fact that private means private, and public means public.