No. I test their convictions myself. I know my character's personality and what other aspects might come to bear. I know his background. I know his game play up to this point.
If my character has sworn an oath never to lie, that matters. If during the game it comes to pass that if he tells the truth about something, a little girl will be killed, that creates a dilemma. Looking at him, I also know that he is a kind and caring person, so how do I reconcile those two aspects that are in conflict. Doesn't hold true to his oath, or does he lie to save the girl. I don't know, but I will struggle with it and eventually come to a decision, but until I make that final decision based on all the information I know, it could go either way.
If I leave it to a die roll, there is no struggle. None at all. Some 20 sided die made the decision independent of the character, taking absolutely nothing into consideration about who he is.