This is nonsense. A key purpose of the First Amendment is to deprive the government of the power to punish a media company because of a dislike of its expressed viewpoint. The most common type of punishment is taking away a privilege.

Were you correct, state governments could punish media companies their governors disagreed with by taking away journalist's driving privileges.

It's also wrong to say "nobody is preventing CNN from broadcasting whatever they like". One of the most common ways those in authority prevent people from doing things is by making clear they will take away a privilege if they do it. One of the key ways we prevent people from driving drunk is by taking away their driving privileges if they do.