This is a weird one. I can't possibly speculate as to the specifics, but it seems to me the explanation most consistent with the facts we have is that SP was, indeed, victimized, but in the course of doing something that she doesn't want LE to know about. In that case, she also wouldn't want LE to find her captors, since that would give them insight into whatever it is she was doing, whether that "whatever" was drug-trade related, some kind of high-class sex work, or something else.
I've come to that conclusion because it is too far-fetched for me to believe that this woman did this to herself or allowed this to be done to her as part of some organized con job. On the other hand, there's a lot that doesn't add up, and the history of dishonesty does give me pause.
The oddest thing for me at this point is figuring out why the kidnappers would have let her go. Crossing someone in the course of serious criminal activity is the kind of thing that tends to get you killed, not chained, beaten, branded and released. I know LE has ruled out sex trafficking, but a) they could be deliberately misleading the public and b) maybe they just mean "as a matter of public safety, we've ruled out the idea that this random woman was snatched from the street." Because wanting to traffic her would be one reason to keep her alive. Someone in an earlier thread suggested that the kidnappers wanted to traffic her, but realized they couldn't do so safely given the publicity the case had gotten. That sounds like a reasonable theory to me. Maybe SP was meeting with some unsavory people who decided they could make money off of her. Before they had passed her on to someone else, however, she became too hot to handle. They didn't feel that they could safely let her go right away, either (or both) because the case was too big, they had to strategize how to do it, or because they thought if they let her go before instilling the fear of God into her, she might spill to the police even at risk of exposing her own prior activities. But they also haven't actually killed anyone before, and aren't willing to cross that line. So, they keep her locked up and beat her -- but don't sexually assault her, since they don't want their DNA anywhere near her. Then, after some time has passed, they let her go.
One detail I think is a red herring in all of this is KP's claim that he told the kids their mom would be home by Thanksgiving. That's a really dumb thing to tell your kids, if you don't know where your wife is, but it would be, IMO, even dumber to tell the press that you had told your kids that if the reason you know she's coming home is that you're in on it. So, of two implausible options, the one in which he actually didn't know where she was is the less absurd one.