Daytime soaps used to be much more important in the lives of people (especially housewives), so you often heard people refer to "my stories," a reference back to when they were on the radio that carried over when they transitioned to TV. Actually, I would say the reason they became known as "stories" rather than identified as "soaps" or "programs" early on was because radio soaps had only dialogue to rely upon, much like someone reading a story aloud rather than watching something being acted out. But the soaps became such an important emotional outlet and such a part of their day/routine that I can see why they'd say "my" stories. They were not watching/listening to those soaps with a group; they were typically alone at home with only the kids (if there were any), so they might say the soaps were "my" personal, daily event/experience.