Leaders communicate wherever people are already reading and listening.
Today, Twitter is just as important of a conduit as newspapers or the evening news.
People already read Twitter and find it far more convenient to follow a world leader than to visit individual sites or set up an RSS reader.
Also you might be suffering from a legal misunderstanding -- Twitter doesn't get any kind of monopoly, free or otherwise, on someone's tweet. You keep the rights to your tweet.
There's zero difference between journalists reporting on a press conference and reporting on a tweet, except that tweets are instant while press conferences take time to set up.
And also that tweets are direct to the public, while when you read a journalist's article they might be omitting parts or spinning it.