There are many, many things that are totally legal for private companies to do but the government is implicitly or explicitly prohibited from doing. Freedom of speech (not saying this is an example of that) is probably the prime example.

A company can bar you from saying just about anything. You can be fired for wearing a tie your boss doesn't like (this never happens, but it's legal in 49 states). The government has very narrow parameters in which is can limit speech, or more accurately, punish you for given speech.