Think of free speech as a noun. Perhaps it should be written as free-speech. What this means is that 1st Amendment protections don't apply to all forms of speech, only free-speech. Examples of things that are not considered free-speech are trade secrets, hate speech, and libelous/slanderous speech. Congress and the States can regulate and pass statutes on those as they wish. They are not afforded Constitutional protection.

The 1st Amendment doesn't grant me the right to write what I want on this forum, even if it would fit in the free-speech classification. Paul Graham can take down whatever he wants, whenever he wants. If Paul Graham became governor of California, he couldn't pass a statute that banned talking about Twitter and TC in online forums. That would run afoul of the 1st Amendment.

I am not sure that I understand your question on how Twitter could go after TC. How would anyone go after another entity without Federal or State law? I doubt there is a local ordinance about this wherever those two companies are located, and I doubt International Law would apply.

If Twitter wanted some sort of non-legal recourse, they could 1) talk it out with TC, 2) reach an out of court settlement, or 3) start the first SMS-organized boycott of a web site.