While speech provides rich, non-invasive biomarkers for mental-health assessment, clinical adoption is limited by opaque models and potential demographic bias. In this work we propose a methodological framework to evaluate robustness and interpretability for automated depression detection on the extended DAIC-WOZ dataset using low-complexity machine learning baselines (RF, SVM, and MLP) chosen to mitigate overfitting and enhance generalization in combination with human-understandable acoustic features (MFCCs, eGeMAPS). To balance accuracy with clinical trust, we leverage explainability methods (LIME and SHAP) for feature selection, validating our findings with statistical significance tests and demographic fairness analyses to mitigate spurious, artifact-driven correlations. Empirical results demonstrate that an optimized subset of explainable AI (XAI)-selected features combined with an MLP architecture achieves a state-of-the-art test accuracy of 82\%. Ultimately, this work provides a transparent framework for robust and ethical assistive technologies that can be applied to any other binary task.