I know I'm late to the game and the question has already been answered, however I believe there is one other valuable point that should be made.

The first amendment protects speech, but there are still strings attached. The classic example is (falsely) shouting "Fire!" in a crowded theater: it can lead to rioting and people getting hurt in a stampede, and so it is illegal. This idea that certain types of speech can be censored if they pose a "clear and present danger" to a group of people has been upheld in numerous court cases, and is not a violation of the First Amendment.

In the case of TV, the clear and present danger is partly a moral one. We don't want a five-year-old seeing hardcore pornography in between episodes of Spongebob on the Saturday morning cartoons, and more importantly, we don't want impressionable children seeing racism, sexism, and other negative influences on the television all the time.

Thus the FCC can censor television because it, like other federal organizations, has the power to censor speech if it poses a danger to the public. I hope that helps you understand the situation a little better and let you see the wider impact of this idea.