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Embodied agents, such as robots, will need to interact in situated environments where successful communication often depends on reasoning over social norms: shared expectations that constrain what actions are appropriate in context. A key capability in such settings is norm-based reference resolution (NBRR), where interpreting referential expressions requires inferring implicit normative expectations grounded in physical and social context. Yet it remains unclear whether Large Language Models (LLMs) can support this kind of reasoning. In this work, we introduce SNIC (Situated Norms in Context), a human-validated diagnostic testbed designed to probe how well state-of-the-art LLMs can extract and utilize normative principles relevant to NBRR. SNIC emphasizes physically grounded norms that arise in everyday tasks such as cleaning, tidying, and serving. Across a range of controlled evaluations, we find that even the strongest LLMs struggle to consistently identify and apply social norms, particularly when norms are implicit, underspecified, or in conflict. These findings reveal a blind spot in current LLMs and highlight a key challenge for deploying language-based systems in socially situated, embodied settings.