I would think that a child who knows enough to look for a therapist, and specifically one that won't tell the parents, would feel reassured by the clarity of 'here's a dollar, you're now officially my therapist' . Especially if there's any history of being lied to or betrayed by adults. Even the small betrayals of promising something, then not fulfilling the promise. Or treating the child seriously to her face, then joking about her to other adults.