Automatic Depression Detection (ADD) from clinical interviews is a pivotal task in computational mental health, yet it remains challenging due to two critical obstacles: 1) difficulty in modeling complex but sparsely distributed depression clues within lengthy, multi-topic clinical interviews, leading to superficial and unreliable reasoning; 2) scarcity of labeled data due to clinical privacy, together with high cost of training and fine-tuning, limiting the deployment of supervised ADD systems. To jointly address these challenges, we propose Dep-LLM, a training-free framework that mirrors the step-by-step reasoning of clinical psychiatrists and operates entirely on frozen off-the-shelf foundation LLMs. Dep-LLM comprises three stages. First, a Chain-of-Thought (CoT) Depression Multi-factor Analysis module structurally decomposes the long dialogue into five clinically aligned themes and produces evidence-grounded rationales, effectively handling long-context dependencies. Second, we introduce Confidence Analysis and Modulation module that quantifies the epistemic reliability from token-level entropy of each rationale and applies an intra-label and inter-theme modulation that amplifies trustworthy signals while suppressing uncertain ones without extra training. Third, a Collaborative Multi-factor Prediction module dynamically integrates multi-factor signals weighted by confidence into the final diagnosis. Extensive experiments on the DAIC-WOZ and E-DAIC datasets demonstrate the effectiveness and generalizability of Dep-LLM: it surpasses zero-shot baseline on nearly all 21 foundation LLMs across 9 metrics such as accuracy, macro F1 and weighted-average F1, and further outperforms state-of-the-art supervised domain-specific LLMs as well as the latest closed-source commercial LLMs, while requiring no extra training.