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Ensemble methods have become the dominant framework for uncertainty quantification in machine learning models for high-entropy alloy (HEA) property prediction, where variance across independently trained neural networks is routinely interpreted as epistemic uncertainty. This metric now underpins active learning, compositional screening, and experimental decision-making, largely due to its simplicity and success in data-rich domains. This work shows that such reliance is fundamentally misplaced in HEAs. Ensemble variance implicitly assumes IID sampling, feature-space isotropy, uniform error, independence among models, and Gaussian residuals—conditions that are systematically violated in compositionally complex alloys. HEA datasets are biased toward equiatomic, stable compositions, the compositional manifold is anisotropic, predictive error is strongly heteroscedastic, ensemble members exhibit correlated failures, and extrapolation induces heavy-tailed errors. Under these conditions, ensemble variance becomes miscalibrated, underestimating uncertainty in sparse regions while overstating model reliability. The resulting distortions propagate through discovery workflows, yielding inefficient active-learning strategies, overconfident extrapolation, and misleading experimental guidance, even as larger ensembles appear to reduce uncertainty without improving accuracy. By linking these failures to their statistical origins, this paper clarifies why standard ensemble diversity is not a faithful proxy for epistemic uncertainty in HEAs. It further outlines diagnostics and targeted corrections that align uncertainty estimates with the physics and data structure of complex alloy systems, enabling more reliable and efficient materials discovery.