Olivia back-stabbed Sloane because....
......she was jealous over the fact that Pete was in love with Sloane and not her. I bet Olivia was in love with Pete, but he was too busy being in love with Sloane that he didn't pay her any mind in that way. I caught a hint of jealousy in Olivia's voice when she mentioned to Pete that she seen him talk to Sloane. I think Olivia threw herself on Pete and Sloane caught them in the act, or Olivia lied to Sloane and tried to make it seem like he wasn't in love with her.
Just a theory.....what are yours?