Broadcast stations have been given the right to use their part of the airwaves for free, a license that would be worth hundreds of millions of dollars if it were auctioned instead of handed out.
In exchange for that, broadcasters agree to operate their stations in the public interest, not as private owners who are entitled to free speech rights. They are heavily regulated, which is why we even have an FCC.
The courts can decide which side is right or wrong on this, but it won't be decided on the basis of first amendment absolutism, because the first amendment is not absolute, and does not apply to those licensed in the public interest.