I hope people can forgive me making an account here specifically for replying lengthily to this post in a somewhat politically tinted way, but I felt compelled to do so because of how wrong i find this comic, and how it completely misses the mark. I lurk this forum for a couple months now if that makes it any better.
The reason why the right to free speech is formulated that way is because it was the moral argument applied to the government, it does NOT imply the moral argument should be limited ONLY to the government because people thought of it so important to set it into law.
To put it another way, the comic assumes free speech flows out of the right of free speech guaranteed by the government, it does not. Its really the other way around, the people (whoever they were) need free speech for our political system to work, so it was decided to enforce at the very least the government, to limit itself through these laws to abide by free speech. Companies were not really a thing yet as they are today.
Taking this logic further with the same driving ideology, if companies become (or would have been at the time) a serious threat to the concept of free speech that just means new methods are needed to guarantee it taking place, be it laws or government alternatives or other solutions.
Before there was no real way competing ideas could force others out of the market of ideas through censorship, you could prevent people from putting flyers in your shop and stuff like that, but if anyone wanted to talk to random strangers on the street about their specific ideology or pet peeve they could do so freely, since the roads belonged to the government.
Roads still do belong to the government, but the roads our ideas move over no longer belong to the government. Facebook, google, chatclients, forums... these are the modern squares where people come to talk. if we give up on free speech there, or not provide a realistic alternative and lose these places, there is no going back. We could very well end up in some cyber punk future where you are guaranteed free speech in your own house and in government provided empty rooms that can be rented for shouting at a wall. If the active squares of political conversation no longer tolerates free speech, then free speech died, no matter its government backing. Denying free speech is in danger is dangerous, naive and callous, simply because our laws are no longer up to date to how political discourse happens.
And don't get me wrong, i do not mean we have to FORCE companies to allow ANYONE to say anything on their platform and EVERYTHING. Or that any forum ever will turn in the_donald. A couple ground rules or some government alternative that can be freely used to debate online in a technologically relevant way would be nice ideas, theres probably better ones out there though..
Free speech is one of the base columns of our society, not just government. If we give that up i guarantee people its only time until we tumble back into oblivion.