If you're already willing to tell a player how his or her character thinks (e.g. "they think the person is lying"), then why do you draw the line at telling a player how his or her character thinks when it comes to Intimidation or Persuasion?
Fine. "He appears to be lying." I am describing what the PC is able to perceive, just like I do in response to any other attempt to interact with the game world they make. A Intuition check made to determine whether or not someone is lying works exactly the same way as a Perception check made against someone who is attempting to physically obscure something (be it their identity via Disguise, their slipping something into a pocket via Sleight of Hand or their actual presence via Stealth). Or do you let your players decide whether or not they can see the thief sneaking through the shadows, too?