There is a finite, shared medium available for broadcasting, like the oceans for instance in shipping. Who owns the oceans? The first people to set anchor in a 4 mile by 4 mile square tract of water? No, it's considered "commons".
The ocean has no owner because it falls outside the political jurisdiction of nation-states. Thus, while one could claim a 4 mile-by-4 mile part of the Atlantic, there would be no government to enforce property rights, opening the pseudo-owner's claim up to piracy or other rival claims. That doesn't mean, however, that property rights could not be established over parcels of water just as they are over land.
But more to the commenter's point, broadcast spectrum is not a "shared" medium by any means. Without the existence of broadcasters to develop the medium, the spectrum is nothing more than hypothetical frequencies which lack form. It is property owners who make broadcasting possible via the spectrum, not "the people" through arbitrary regulation. The fact that the spectrum was not initially privatized—i.e. that spectrum is licensed through the FCC—is due to the coincidental rise of the regulatory state as radio and television technology was invented. The spectrum could have easily been parceled out free of further government obligation, just as the entire Western frontier of America was at one time.