Actually, existing case law argues that this is false in cases where a company controls a public space. This easily could be applied again to online companies.
Marsh v. Alabama, 326 U.S. 501 (1946); Grace Marsh, a Jehovah's witness distributing religious pamphlets vs Gulf Shipbuilding Corporation which owned Chikasaw.
In its conclusion, SCOTUS stated that it was essentially weighing the rights of property owners against the rights of citizens to enjoy freedom of press and religion. The Court noted that the rights of citizens under the Bill of Rights occupy a preferred position. Accordingly, the Court held that the property rights of a private entity are not sufficient to justify the restriction of a community of citizens' fundamental rights and liberties.
See https://en.wikipedia.org/wiki/Marsh_v._Alabama