Deep neural networks often suffer performance degradation upon deployment due to distribution shifts. Continual Test-Time Adaptation (CTTA) aims to address this issue in an unsupervised manner. However, existing methods that rely on self-supervision are prone to an inherent self-referential feedback loop that amplifies initial prediction errors, leading to model drift. We revisit this limitation and propose Test-Time Distillation (TTD), which reframes adaptation as a distillation process guided by a frozen Vision-Language Model (VLM) as an external signal. While promising, we find that direct distillation is fraught with two pitfalls: (1) the Generalist Trap, where the VLM's broad but non-specialized knowledge leads to suboptimal performance on specific tasks and shifts; and (2) the Entropy Bias, where naive model fusion techniques based on entropy fail due to the disparate calibration of heterogeneous models. These pitfalls highlight the need to build a robust supervisory signal and leverage it to guide the target model toward stable adaptation. Hence, we present CoDiRe, a Continual Distillation and Rectification framework for TTD. CoDiRe first constructs a robust blended teacher by dynamically fusing the predictions of the VLM and the target model. Critically, it circumvents the Entropy Bias by leveraging Maximum Softmax Probability (MSP) as a more reliable confidence metric for weighting each model's expertise. Then it applies an Optimal Transport-based rectification to further align predictions with the blended teacher, enabling continuous and stable adaptation. Extensive experiments show that CoDiRe outperforms state-of-the-art baselines, exceeding CoTTA by 10.55% with only 48% of its time cost on ImageNet-C. Project page is publicly available at https://github.com/walawalagoose/TTD.