Final answer:
The therapist's approach described in the case study aligns with client-centered therapy, which necessitates a non-judgmental and value-neutral stance, allowing the client to feel accepted and understood.
Step-by-step explanation:
The therapist's approach of assuming an anonymous non-judgmental stance is indicative of client-centered therapy, developed by Carl Rogers. This therapeutic method emphasizes the importance of a therapist providing unconditional positive regard, genuineness, and empathy. The non-judgmental stance is part of creating a safe and accepting environment for the client, aligned with the practice of value neutrality, which involves remaining impartial and without bias during a study or therapeutic process.