Language-supervised pre-training has proven to be a valuable method for extracting semantically meaningful features from images, serving as a foundational element in multimodal systems within the computer vision and medical imaging domains. However, resulting features are limited by the information contained within the text. This is particularly problematic in medical imaging, where radiologists' written findings focus on specific observations; a challenge compounded by the scarcity of paired imaging-text data due to concerns over leakage of personal health information. In this work, we fundamentally challenge the prevailing reliance on language supervision for learning general purpose biomedical imaging encoders. We introduce RAD-DINO, a biomedical image encoder pre-trained solely on unimodal biomedical imaging data that obtains similar or greater performance than state-of-the-art biomedical language supervised models on a diverse range of benchmarks. Specifically, the quality of learned representations is evaluated on standard imaging tasks (classification and semantic segmentation), and a vision-language alignment task (text report generation from images). To further demonstrate the drawback of language supervision, we show that features from RAD-DINO correlate with other medical records (e.g., sex or age) better than language-supervised models, which are generally not mentioned in radiology reports. Finally, we conduct a series of ablations determining the factors in RAD-DINO's performance; notably, we observe that RAD-DINO's downstream performance scales well with the quantity and diversity of training data, demonstrating that image-only supervision is a scalable approach for training a foundational biomedical image encoder.