I think I could accept "I do not like stories" (in general), added. I also guess I can't totally reject the singular interpretation, although it's a lot less likely. But for "I do not like the story" (I don't like the story that I'm hearing right now, right?) that should take another verb "Nie podoba mi się ta historia" (yeah, better make it 'this story' or otherwise it's "lubić" is for general things, for some more longterm opinion. Perhaps it could be "I don't like the story" if we're talking about a video game and you love the graphics and the gameplay but not the story, so it's now a general opinion about a game you already know well.