Clear Channel: Whose Freedom?

According Salon Magazine, Clear Channel, the radio and concert behemoth, “barred protest groups from distributing literature at an Ani DiFranco concert in New Jersey — and threatened to pull the plug on DiFranco or anyone else who made antiwar comments from the stage.”
Clear Channel is trying to stop musicians and fans from speaking against the war, at the same time that they sponsor pro-war rallies.
Obviously their behavior is notorious. In the grand old Hearst tradition of yellow journalism, they’re flogging a war in order to sell add space. At the same time, they’re repressing anti-war speech.
But is this censorship? Censorship is typically construed to apply to government actions.
Does the concept of censorship also apply to commercial players who have overwhelming market share in a medium of speech? Or is Clear Channel free to make any business decision with their own property?
Clear Channel is the dominant player in radio. “Clear Channel owns over 1,200 radio stations and 37 television stations, with investments in 240 radio stations globally, and Clear Channel Entertainment (aka SFX, one of their more well-known subsidiaries) owns and operates over 200 venues nationwide. They are in 248 of the top 250 radio markets, controlling 60% of all rock programming.”
Clear Channel has enough market share in the radio industry to be able to silence musicians’ political speech at the cost of the musicians’ livelihood.
Do musicians have any recourse, other than to and make their living in another field? Do consumers and citizens have any recourse, other than to turn the radio off and not go to concerts?
Does freedom of the press belong to he who owns the press, over and out?