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LLM-based explainable recommenders can produce fluent explanations that are factually correct, yet still justify items using attributes that conflict with a user's historical preferences. Such preference-inconsistent explanations yield logically valid but unconvincing reasoning and are largely missed by standard hallucination or faithfulness metrics. We formalize this failure mode and propose PURE, a preference-aware reasoning framework following a select-then-generate paradigm. Instead of only improving generation, PURE intervenes in evidence selection, it selects a compact set of multi-hop item-centric reasoning paths that are both factually grounded and aligned with user preference structure, guided by user intent, specificity, and diversity to suppress generic, weakly personalized evidence. The selected evidence is then injected into LLM generation via structure-aware prompting that preserves relational constraints. To measure preference inconsistency, we introduce a feature-level, user-centric evaluation metric that reveals misalignment overlooked by factuality-based measures. Experiments on three real-world datasets show that PURE consistently reduces preference-inconsistent explanations and factual hallucinations while maintaining competitive recommendation accuracy, explanation quality, and inference efficiency. These results highlight that trustworthy explanations require not only factual correctness but also justification aligned with user preferences.