Large language models (LLMs) are increasingly used for causal and counterfactual reasoning, yet their reliability in real-world policy evaluation remains underexplored. We construct a benchmark of 40 empirical policy evaluation cases drawn from economics and social science, each grounded in peer-reviewed evidence and classified by intuitiveness -- whether the empirical finding aligns with (obvious), is unclear relative to (ambiguous), or contradicts (counter-intuitive) common prior expectations. We evaluate four frontier LLMs across five prompting strategies with 8,000 experimental trials and analyze the results using mixed-effects logistic regression. Our findings reveal three key results: (1) a chain-of-thought (CoT) paradox, where chain-of-thought prompting dramatically improves performance on obvious cases but this benefit is substantially attenuated on counter-intuitive ones (interaction OR = 0.278, p<0.001); (2) intuitiveness as the dominant factor, with case-level variance exceeding that of model choice or prompting strategy (ICC = 0.671); and (3) a knowledge-reasoning dissociation, where citation-based familiarity is unrelated to accuracy (p=0.84), suggesting models possess relevant knowledge but fail to reason with it when findings contradict intuition. We frame these results through the lens of dual-process theory (System 1 vs. System 2) and argue that current LLMs' "slow thinking" achieves only partial inhibition of intuitive priors -- producing the form of deliberative reasoning without fully delivering its substance.