This is true, but the first amendment should also prevent the government from pressuring said companies to censor speech as well. This would be the government using it's power and coercion to violate people's 1st amendment rights via a third party. Think "hiring someone to murder someone is still murder for the person hiring," or a police soliciting a trespass.

The recent "Twitter files" showed that the government is/was working directly with Twitter and probably all the media companies to censor speech. The government, on multiple occasions, provided specific tweets and people to censor and Twitter complied. I believe they had weekly meetings to do just that.