When does an AI assistant improve human decision-making, and when does it hurt? We argue that the answer depends not just on AI accuracy but also on how much its evidence overlaps with the human's and how the human combines the two. A worker makes a binary decision by observing her own signal and receiving a recommendation from an AI. We develop a human behavioral model with two primitives: her awareness of the overlap and her trust in the AI. Our analysis gives a closed-form phase diagram over AI capability and overlap, with regions of complementarity, impairment, and automation. A worker who neglects the overlap (correlation neglect) can be made less accurate by a more capable AI, double-counting the shared evidence. Trust reshapes the regions - undertrust may compensate for correlation neglect, so that the trust level maximizing accuracy depends on the deployment parameters. Empirically, we identify the two model parameters by pairing the same workers with different AIs, and break the accuracy loss into a correlation-neglect cost and an undertrust cost, one tied to reducing overlap on the AI side, the other to calibrating trust on the human side. On ChatBench, AI assistance raises accuracy by 21 points, yet workers apply only about a quarter of the Bayes-rational weight to AI information; GPT-4o falls in the automation region and Llama-3.1-8b stays at the complementarity boundary; and calibrating trust recovers about 2.6 points for GPT-4o but almost nothing for Llama-3.1-8b.

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