Not entirely correct. In most cases you would be right, but if someone can prove that a service represents a monopoly, or such a dominating hold on a field that the inability to use it to express yourself is an unreasonable barrier to your free expression, then a court might hold that the company policy is a "de facto law", and therefore, must be subject to the same standards as a "de jure law"

Take this example; you live in an area serviced by only one ISP. That ISP decides that it is not going to allow people in your area to access a political website you have put up. There are no other options for you, so even though the ISP is a private company, they have hampered your ability to engage in local politics, and therefore, have violated the first amendment by introducing a new "law" without going through congress.

I can't think of a case off of the top of my head where this has been used on the first amendment. Generally it was used to combat racial discrimination in housing, where large parts of a city would have a "no blacks allowed" policy for renters. It has some interesting caveats, and generally it requires "use of a government appartus to enforce a de facto law", e.g. using the police to remove black tenants.

Still, I think its a concept worth expanding upon in this climate of telecommunication oligopolies. There are plenty of mediums of expression where you actually don't have that many choices in who you do business with (smartphone apps for example), and if we're not going to do the right thing and actually regulate monopolies, we could at least hold their corporate policies to a higher standard than in businesses where there is actually competition.