Large language models often produce hallucinated answers that violate prompt-level constraints. A key diagnostic question is whether these failures reflect missing knowledge, or whether the model has the relevant information but follows the wrong inference path. We study this phenomenon as *inference misalignment*: a mismatch between the answer supported by the prompt and the answer favored by statistically salient latent associations. We formalize this view with a latent key–task model, in which pretraining-frequency imbalance can cause a shortcut path to dominate the constraint-sensitive path and induce positive inference loss. The framework predicts two failure modes: task-retrieval bias in entity disambiguation and key-selection bias in action choice. We introduce *TrapQA*, a controlled diagnostic testbed with two components. *ScientistQA* tests disambiguation among similar scientists with supplementary factual probes, while *Real-Life Constrained QA* tests everyday constraint following under salient shortcuts. Our results show that hallucination can arise from biased latent inference rather than absent knowledge alone.