Re-reading the definitions, I've decided that maybe the Los Angeles Times made the wrong call when they referred to several different types of news media as "mediums." (Maybe they were too hasty, as was I in interpreting the meaning of all this.) Here's the full definition from the Times' go-to dictionary, Webster's New World. Note that it offers separate definitions for the plural of forms of communciation than it does for clairvoyants. 

medium definition me·dium (mē′dē əm)

noun pl. mediums -·di·ums or media -·dia (-ə)

1. a. something intermediate; b. a middle state or degree, mean
2. an intervening thing through which a force acts or an effect is produced 'copper is a good medium for conducting heat'
3. pl. media: any means, agency, or instrumentality; specif., a means of communication that reaches the general public and carries advertising: in this specif. sense, a singular form media (pl. medias) is now often used
4. any surrounding or pervading substance in which bodies exist or move
5. environment
6. a sterilized nutritive mixture, as enriched agar, for cultivating bacteria, viruses, etc.
7. pl. mediums me′di·ums☆ a person through whom communications are thought to be sent to the living from spirits of the dead
8. any material or technique as used for expression or delineation in art
9. a liquid mixed with pigments to give smoothness