The presence of a single non-exempt purpose, if more than insubstantial in nature, will destroy the exemption of the organization regardless of the number or importance of truly exempt purposes that are present.
So even assuming the most doubtful proposition that a news organization has a right to speak when others do not, the exemption would allow a conglomerate that owns both a media business and an unrelated business to influence or control the media in order to advance its overall business interest.