The scalability of current language-image pre-training for 3D medical imaging, such as CT and MRI, is constrained by the need for radiologists to manually curate raw clinical studies. In this work, we pioneer pre-training directly on uncurated studies, which both aligns more closely with the radiologist's workflow and provides a natural path to scalability. However, the unique structure of such data presents new challenges for existing model architectures, which were originally designed for 2D slices or single 3D scans. To address this, we introduce a novel hierarchical attention mechanism inspired by the intrinsic hierarchy of radiology data: slice, scan, and study. We denote our framework as Hierarchical attention for Language-Image Pre-training (HLIP). Trained on 220K studies with 3.13 million scans for brain MRI and 240K studies with 1.44 million scans for head CT, HLIP achieves state-of-the-art performance, e.g., +10.5% balanced ACC on the proposed publicly available brain MRI benchmark Pub-Brain-5; +8.3% and +1.7% macro AUC on head CT benchmarks CQ500 and RSNA, respectively. HLIP also exhibits strong generalizability on existing 3D medical language-image pre-training benchmarks, e.g., +4.3% macro AUC on the Rad-ChestCT benchmark when pre-trained on CT-RATE. These results demonstrate that, with HLIP, directly pre-training on uncurated clinical datasets is a scalable and effective direction for language-image pre-training in 3D medical imaging. The code is available at https://github.com/Zch0414/hlip.