From a free speech/free press standpoint, private company Twitter absolutely has the right to editorialize Trump's tweets, while Trump trying to silence Twitter would be the government infringing on the right to free speech/press.
But if that were true then they would be personally liable in a court of law for tweets that break the law. Seems like they want to be treated as both an "editor" with the right to change user content and "just a distribution platform". They can't have it both ways.