Freedom of speech isn't a law, it is a concept. If you are in a private space and insult someone, they may choose to not 'turn the other cheek'. Does that mean 'turning the other cheek' can't be applied in private spaces? They are both concepts, not laws.
This is so abstract as to be meaningless, I have no idea what you're arguing or what you think "applied" means in this context. Does the concept of "free speech" mean you ought to be able to scream the n word in a Wendy's without being asked to leave? If not, my point is that Twitter is no different; if yes, then you and I mean very different things by "free speech".
It is abstract, and the argument is semantic. Freedom of speech is an concept, turning the cheek is a concept. Most people agree neither should be applied absolutely, but they both can be applied or ignored in any space, private or public.
There are laws that try to codify the concepts. The 1st amendment is one of such laws, but it only applies to the US government. It doesn't mean that the concept it is based on is held to the same restrictions.
