High internal AUCs (>0.95) are frequently reported for Alzheimer’s disease (AD) classifiers, yet such models often fail under clinical deployment. We attribute this gap to two compounding issues: (i) data leakage that inflates internal metrics and (ii) untested domain shift across cohorts. We introduce a leak-safe validation protocol with five mandatory safeguards and evaluate it on 3,238 subjects from OASIS-3 (population-representative; 23% AD; natural age distribution) and ADNI (trial-enriched; 72% AD; age-matched). Using FastSurfer-derived MRI morphometric features (and MRI+PET within-cohort analysis in OASIS), leak-safe models achieve realistic within-cohort performance (AUC 0.77–0.94) with limited age confounding (1.3–4.2% AUC contribution). We then perform strict bidirectional external validation without retraining. Training on ADNI and testing on OASIS-3 yields severe collapse (AUC 0.894→0.535; PR-AUC 0.32), whereas training on OASIS-3 and testing on ADNI shows upward generalization (AUC 0.838→0.851; PR-AUC 0.94). A sample-size learning curve in the ADNI→OASIS direction (N=142–571; six stratified subsamples) shows degradation does not decrease with more data and instead correlates positively with training size (Pearson r=0.847, p=0.033), suggesting larger trial-enriched sets increasingly internalize source-specific biases. Feature stability analysis identifies hippocampus/ICV ratio as the most cross-cohort stable biomarker. Overall, distributional mismatch—not data insufficiency—dominates cross-cohort generalization limits and is critical for deployment readiness.