Yes, that was one part of the point I was making. The other is that the left want to have it both ways. They want to argue that because of the point you made, corporations have a duty to provide the same kind of freedoms that governments are required to allow in public forums. On the other hand, when right wingers are censored by corporations, they deny that there is any duty for a private corporation to provide a venue for people to express speech that the corporation doesn't allow.

EDIT: e.g. jjaredsimpson's downvoted comment would probably not be downvoted if this article was about a "racist" post being removed from facebook.