LLMs promise to overcome limitations of rule-based mental health chatbots through improved natural language capabilities, yet their ability to deliver evidence-based psychological interventions remains largely unverified because evaluations rarely apply the validated fidelity measures used to assess psychotherapists. We developed an LLM-based chatbot that delivers behavioral activation for depression and generated 48 complete chat sessions with diverse artificial users. Ten psychotherapists assessed these sessions using the Quality of Behavioral Activation Scale (Q-BAS), a validated fidelity instrument. Results show that the chatbot reliably executed the intervention across all phases and maintained safety protocols, but it struggled with clinical judgment, particularly when verifying the feasibility of proposed activities. Overall, our findings suggest that LLM-based chatbots can execute therapeutic protocols with high fidelity, while robust clinical reasoning remains an open challenge. We outline design implications to address this gap and provide the chatbot and artificial user prompts.