Malcolm,
I dispute not what you say, and you are correct , of course in saying that copyright claims exist on public domain material. My point (or rant if you prefer) is that copyright is the property of the author and if it is not granted to another, it remains with the author until his/her death and to his/her heirs for a proscribed period following. It then comes into the public domain. A claim of copyright is often made by people or organizations , and this usually has less to do with claiming ownership than collecting royalties. In such cases they would be more interested in recording royalties than performance royalties, but if they are entitled to one the other would follow. If people willingly pay these royalties then the money rolls in. If they refuse then ownership would have to be proven by civil testing (on the balance of probabilities ) in a court of law.
   I can make a claim to 40 acres on the surface of the moon , and if a couple of Martians are happy to pay me 600 loons a month in rent.I would be happy also. If they refuse to pay then I may have a problem establishing that I have titled ownership.
Copyright laws , while bound by international convention, may be very different in different countries so I only speak in generalities.
                  Obie