Not "the public."

And not "private", in particular if those 30 people actively trade said stock (i'll ignore the legal side of trading share of a car, because it's irrelevant in horrible car analogies). But ultimately, the point Giz was making is that those corporations are traded by public, owned by no one in particular (in fact, often biggest shareholders of those corporations are other corporations or some proxy organizations) , and often receive government funding. Calling them 'private' is really an abuse of notation.

Still not owned by "the public."

These people don't own the car either. They (each) own part of the car, a different thing.

A house is for sale on the open market. Three people chip in to buy it and live there. Who owns it (let's assume it was a cash sale)?

Don't know, but i know down here a solid part of first degree murder cases are property dispute, so i suspect these people wouldn't know either.