One of the big lies of the TV business is that "reality shows" are unscripted. Just about every such show has a couple of folks who oughta have the title of Writer but aren't called that because the producers don't want to work under the auspices of the Writers Guild of America, West. I'm not sure how much of this is because they want to pretend everything on the show is spontaneous and how much is because they just don't want to pay WGA rates and abide by the list of things that the WGA says you can't do to its members.
It doesn't have to be like this, of course. Some "reality shows" (I'm deliberately using the quotes) are WGA signatories and in the eighties, when the term was coined for a certain new kind of program, almost all were, including a show I worked on. We wrote narration. We wrote seeming ad-libs for the on-camera participants. We also helped work out scenarios for what would be filmed and helped structure the storylines created in the editing room.
It is not true that a "reality show" points its cameras at things that would have happened even if the video crew wasn't present. Someone arranges for the participants to be there, someone "casts" them, someone plots (in the same way a writer plots a screenplay) the challenges and problems they will confront. Writers may or may not write some of what the people say, and of course someone writes narration and introductions and voiceovers. In the editing process, the footage is structured to create a narrative and during that process, someone may be doing much the same kind of work that a Writer does when involved in the editing process on a fiction show.
The Writers Guild is attempting to bring down the lie that "reality shows" don't have Writers. One effort towards that end is this video, which explains how Writers participate in the creation of the WGA-signatory series, Intervention. Give it a look…