kellan media

If what you say is true and writers are actually working in the 'unscripted' world, then where are the writers on a Reality Show?

A reality show's writers are  segment producers or story editors . These producers do all the writing: assemble storyboards and shooting scripts as well as participating in the editing.
In the scripted world  Segment Producers would be known as writers. But unlike writers, they're generally not recognized by the Writers Guild of America and so aren't union employees.

This distinction could be seen as a disservice to the segment producers and story editors, but it benefits the show in that it lowers production costs -- and it helps preserve the idea that the shows are real and unscripted.