While speech-based depression detection methods that use speaker-identity features, such as speaker embeddings, are popular, they often compromise patient privacy. To address this issue, we propose a speaker disentanglement method that utilizes a non-uniform mechanism of adversarial SID loss maximization. This is achieved by varying the adversarial weight between different layers of a model during training. We find that a greater adversarial weight for the initial layers leads to performance improvement. Our approach using the ECAPA-TDNN model achieves an F1-score of 0.7349 (a 3.7% improvement over audio-only SOTA) on the DAIC-WoZ dataset, while simultaneously reducing the speaker-identification accuracy by 50%. Our findings suggest that identifying depression through speech signals can be accomplished without placing undue reliance on a speaker's identity, paving the way for privacy-preserving approaches of depression detection.