Since virtually all media in the U.S. is 'private companies', that argument is one of the more stupid ones re censorship. If one wants to use that as a pretext for censorship, then there is no point in giving the 'Press' special rights and 'freedoms' it has traditionally benefited from. Since the majority of the MSM isn't a 'fourth estate' any more, just tabloid propaganda hacks, we're pretty much 'there' anyway.
If all property in the U.S. were to end up being owned by just a small number of people, say 3 or 4, then 'private property' becomes a meaningless 'right' for 'everybody else', only being exercisable for those 3 or 4, and will disappear on its own as a 'right'; it will no longer have any mass support.
For further reading: Democratic Socialists of America