A person who has experienced personal conversion has been through this process. You realize that you are more sinful that you dared to believe. And that God does, in fact, know you to the core of your being. Yet he still loves and forgives. Jesus went through an extremely shameful experience (crucifixion) though he did not deserve it at all, and he did this so that we who did deserve it would experience God's unconditional acceptance and love toward us. So a person who is a Christian has felt the healing power of God's love toward them, even in the midst of their shame.
Therefore, when a person reveals their own shame and their own secrets. Christians are positioned to say, "I too know what it is like to carry shame, and I also know what it feel like to be forgiven, loved and accepted." This gives Christians incredible resources to bring healing into the lives of those dealing with shame.