Self-supervised representations excel at many vision and speech tasks, but their potential for audio-visual deepfake detection remains underexplored. Unlike prior work that uses these features in isolation or buried within complex architectures, we systematically evaluate them across modalities (audio, video, multimodal) and domains (lip movements, generic visual content). We assess three key dimensions: detection effectiveness, interpretability of encoded information, and cross-modal complementarity. We find that most self-supervised features capture deepfake-relevant information, and that this information is complementary. Moreover, models primarily attend to semantically meaningful regions rather than spurious artifacts (such as the leading silence). Among the investigated features, audio-informed representations generalize best and achieve state-of-the-art results. However, generalization to realistic in-the-wild data remains challenging. Our analysis indicates this gap stems from intrinsic dataset difficulty rather than from features latching onto superficial patterns. Project webpage: https://bit-ml.github.io/ssr-dfd.