Artificial intelligence (AI) shows great potential in assisting radiologists to improve the efficiency and accuracy of medical image interpretation and diagnosis. However, a versatile AI model requires large-scale data and comprehensive annotations, which are often impractical in medical settings. Recent studies leverage radiology reports as a naturally high-quality supervision for medical images, using contrastive language-image pre-training (CLIP) to develop language-informed models for radiological image interpretation. Nonetheless, these approaches typically contrast entire images with reports, neglecting the local associations between imaging regions and report sentences, which may undermine model performance and interoperability. In this paper, we propose a fine-grained vision-language model (fVLM) for anatomy-level CT image interpretation. Specifically, we explicitly match anatomical regions of CT images with corresponding descriptions in radiology reports and perform contrastive pre-training for each anatomy individually. Fine-grained alignment, however, faces considerable false-negative challenges, mainly from the abundance of anatomy-level healthy samples and similarly diseased abnormalities, leading to ambiguous patient-level pairings. To tackle this issue, we propose identifying false negatives of both normal and abnormal samples and calibrating contrastive learning from patient-level to disease-aware pairing. We curated the largest CT dataset to date, comprising imaging and report data from 69,086 patients, and conducted a comprehensive evaluation of 54 major and important disease (including several most deadly cancers) diagnosis tasks across 15 main anatomies. Experimental results demonstrate the substantial potential of fVLM in versatile medical image interpretation. In the zero-shot classification task, we achieved an average AUC of 81.3% on 54 diagnosis tasks, surpassing CLIP and supervised methods by 12.9% and 8.0%, respectively. Additionally, on the publicly available CT-RATE and Rad-ChestCT benchmarks, our fVLM outperformed the current state-of-the-art methods with absolute AUC gains of 7.4% and 4.8%, respectively.