I think Kim called various escort services trying to figure out where the accuser lived. Maybe she drove to a wrong address. I don't know what they did but I doubt they concocted a story. Kim's goal was to get rid of the accuser and she even had the police called to do it. She then said what she had to in order to get herself out of the situation. She then left. She didn't care what the cops did with the accuser.
The cops who initially saw Precious did not believe her story. That seems clear to me. Someone at Duke was informed that the entire thing would blow over and one of the reasons was that Precious had no credibility. They probably knew who she was if she's had this many encounters with the police. They didn't push to get a search warrant or do anything. I don't think they believed her at all.
I think the set-up, if you want to call it that, started when someone else came into the picture and decided to push this case. Nifong had a political motive. Gottlieb clearly hates Dukies. I think they're the ones who set this up. I don't think Kim and Crystal set it up themselves.
You have it exactly right. The villan is Nifong. He had the primary coming up. We don't need to be looking for any involved conspiracies theories although certainly some of the DPD has jump in to aid Nifong all they could.