Health systems are rapidly deploying generative-AI assistants that answer patient questions from institution-authored education materials, on the premise that grounding in local content yields consistent guidance. Do the underlying documents themselves agree? We use a structured-output large-language-model judge to audit 1{,}772{,}261 pairwise comparisons across 102 patient-education handbooks from 23 US solid-organ transplant centers, paired with 1{,}115 patient-derived questions (TransplantQA). Four findings bear directly on deployment: (1) same-center cross-organ agreement exceeds cross-center same-organ agreement by $0.024$ in the primary analysis (Holm-adjusted $p=0.011$), with sensitivity to document selection; (2) information gaps concern topics relevant to underrepresented subgroups, with reproductive health a \emph{double jeopardy}: 82\% absence and 86\% judge-rated high significance among divergent/contradictory pairs; (3) judge-derived themes form 991 clusters, with immunosuppression and pregnancy timing among the highest judge-rated priorities; (4) question and observed-coverage features predict high-divergence questions retrospectively (AUC $0.77$). We discuss implications for deploying patient-facing generative AI in transplant care.

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