>The same rules of freedom of speech should apply there.
If you want freedom of speech to apply in privately controlled media, you would have to compel them to distribute content they do not agree with, which is itself a violation of freedom of speech.
And this is the problem with a simplistic idea like "Freedom of Speech". It is not possible for everyone to hear everyone else's point of view, so some speech will always be restricted. Therefore, our society inevitably makes decisions about which speech to amplify and which to silence, and just because that decision is not being made directly by government, does not mean it is not being made.
In practice when people complain about censorship, what they mean is that these implicit decisions are not being made in a way that they like. And in saying this, I'm not trying to imply that their criticisms are wrong, or that they're being disingenuous or malicious in trying to change those decisions. I'm saying this to reframe the debate, because framing it as if access to speech can only be controlled by intentional malicious restriction prevents us from questioning the ways in which society already controls access to speech.
The most common way speech is restricted is economic. The rich can afford to amplify their speech, and the poor cannot. We have historically accepted this without question as an economic reality, but then the rise of social media gave us a glimpse of a world where economic restrictions are not as big a factor, and so when these restrictions start to re-assert themselves we question them.
People call it "censorship" and demand "free speech", because this is the most pervasive set of ideas we have to understand this dissonance, but the reality is we are always censored, and speech is never truly free, and unless we accept that, we will not be able to ask real questions about what kind of societal discourse we truly value.