1) Background: As Machine Learning (ML) transitions from theoretical benchmarks to clinical implementation, the role of Explainable AI (XAI) has evolved from a technical preference to a core requirement for trust and accountability. A significant obstacle remains: the empirical stability of these explanations is often untested against the noise and imperfections inherent in real-world patient data. (2) Methods: This study evaluates the stability of SHAP (SHapley Additive exPlanations) under systematic data perturbations—including Gaussian noise and structured feature omission—using a 1,100-patient Pan-Cancer cohort from the TCGA Atlas. We utilise a dual-metric framework to assess consistency in feature selection (Jaccard index) and ranking (Spearman correlation). (3) Results: SHAP-based attributions maintain an aggregate Jaccard index of 0.778 and a Spearman correlation of 0.858 across various noise intensities, establishing their resilience in high-dimensional genomic spaces. We propose a Global Stability Index (GSI) of 0.770 as a quantitative benchmark for evaluating XAI reliability in oncology. (4) Conclusions: The consistent identification of the SPRR1B biomarker across diverse simulations confirms that the model captures robust biological signals. These results provide empirical support for integrating XAI into clinical workflows, aligning with the transparency requirements of the EU AI Act.