This article presents HeteroSync Learning (HSL), a novel, privacy-preserving distributed framework designed to overcome the critical limitation of data heterogeneity in distributed Artificial Intelligence (AI) for medical imaging. The research was performed by building the HSL framework around two core components: a Shared Anchor Task (SAT), which uses a uniform public dataset to establish cross-node representation alignment, and an Auxiliary Learning Architecture to coordinate the SAT with the local primary task. This framework was rigorously validated across extensive large-scale simulations covering feature, label, quantity, and combined heterogeneity, as well as a real-world multi-center thyroid cancer study. HSL consistently outperformed local learning, 12 benchmark methods, and foundation models in terms of both efficacy and stability. The framework achieved up to a 40% improvement in Area Under the Curve (AUC) over baselines, matching the performance of a central learning model, and demonstrated superior generalization with an AUC of 0.846 on out-of-distribution pediatric data. Ultimately, this work provides an effective, privacy-preserving solution for distributed medical AI, enabling equitable collaboration across varied healthcare institutions without sharing raw patient data. The authors conclude that HSL is a significant step toward the democratization of AI-driven healthcare, benefiting both resource-rich and underserved populations.