In the context of the Constitution, government censorship is the only thing that the United States cares about.
If we valued banning all censorship we'd make laws banning that. We don't: we value private property and free speech instead. Taking the rights of private parties to control what they publish tramples both of those rights. It's not complicated: you have a right to own your 'press' and do whatever you want with it. You don't have a right to someone else's press.
Censorship is free speech?
No they are saying choosing what to publish or not is part of private property rights.
> censor (verb): to examine in order to suppress (see suppress sense 2) or delete anything considered objectionable.
> also: to suppress or delete as objectionable
Government censorship is a very notable class of censorship, but the word has a broader meaning.