First Amendment, FCC, Clear Channel and Stern

Reading here and at other blogs I've read a number of comments that flatly argue that the First Amendment cannot be implicated by Clear Channel's actions because it is a private actor.

I believe this is incorrect. The First Amendment could certainly be implicated IF Clear Channel's decision to ax Stern resulted from an attempt to curry favor with the FCC. That is, Stern was punished for his speech because the government will favor Clear Channel for censoring Stern's speech.

Sure Clear Channel has a right to put on whomever they like, but they don't have a right to punish speech as a proxy for the government. That would have First Amendment implications.