Nah, none of those networks were anywhere near as influential as Twitter is now. Many reporters basically live on Twitter; it's at the center our media world.
I don't believe in the idea of "entitled to" or not "entitled to" as absolute moral truths. We come up with a set of rules as a society and entitlements come from those rules.
It's perfectly reasonable to imagine various combinations of rules and try to guess which combination will give us the society we like most.
One possible rule is "private companies should be able to do whatever they want under all circumstances," which is what you and several others seem to be arguing here. I'm sympathetic to that viewpoint in the small, but once corporate entities reach a certain scale and omnipresence, I think it ceases to be reasonable -- in the limit as a corporate entity grows large and powerful, it becomes a government. As it approaches that limit, it should be similarly constrained.
Let me give you an example that will probably make you agree with me. Let's say Twitter decides -- since, hey, it's a private entity and can do whatever it wants with its product -- to delete any accounts that some machine-learning algorithm has identified as belonging to racial group X.
Cool or nah?