That's not really accurate. To enjoy "freedom of the press" a person must be considered part of the media. A person who writes a letter to the government is not protected by Freedom of the Press but by Freedom of Speech.
Freedom of speech also is not limited to vocal statements - it also can include writings and actions.
So if I do a neighborhood newsletter once that I place on all my neighbors doors, that is not press? I would think that would fall under the freedom of press clause, but I would not be considered part of the media.