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Human processing of idioms heavily depends on interpreting the surrounding context in which they appear. While large language models (LLMs) have achieved impressive performance on idiomaticity detection benchmarks, this success may be driven by reasoning shortcuts present in existing datasets. To address this, we introduce a novel, controlled contrastive dataset (DICE) specifically designed to assess whether LLMs can effectively leverage context to disambiguate idiomatic meanings. Furthermore, we investigate the influence of collocational frequency and sentence probability—proxies for human processing known to affect idiom resolution—on model performance. Our results show that LLMs frequently fail to resolve idiomaticity when it depends on contextual understanding, performing better on sentences deemed more likely by the model. Additionally, idiom frequency influences performance but does not guarantee accurate interpretation. Our findings emphasize the limitations of current models in grasping contextual meaning and highlight the need for more context-sensitive evaluation.