Open challenges have become the de facto standard for comparative ranking of medical AI methods. Despite their importance, medical AI leaderboards exhibit three persistent limitations: (1) score gaps are rarely tested for statistical significance, so rank stability is unknown; (2) single averaged metrics are applied to every organ, hiding clinically important boundary errors; (3) performance across intersecting demographics is seldom reported, masking fairness and equity gaps. We introduce RankInsight, an open-source toolkit that seeks to address these limitations. RankInsight (1) computes pair-wise significance maps that show the nnU-Net family outperforms Vision-Language and MONAI submissions with high statistical certainty; (2) recomputes leaderboards with organ-appropriate metrics, reversing the order of the top four models when Dice is replaced by NSD for tubular structures; and (3) audits intersectional fairness, revealing that more than half of the MONAI-based entries have the largest gender-race discrepancy on our proprietary Johns Hopkins Hospital dataset. The RankInsight toolkit is publicly released and can be directly applied to past, ongoing, and future challenges. It enables organizers and participants to publish rankings that are statistically sound, clinically meaningful, and demographically fair.