Health data sharing is very valuable for medical research since it has the propensity to improve diagnostics, policy, medication, and so on. At the same time, sharing health data needs to be done without compromising the privacy of patients and stakeholders. However, recent advances in AI/ML and sophisticated analytics have proven to introduce biases that can easily identify patients based on their healthcare data, which violates privacy. In this work, we sort to address this major issue by exploring two emerging topics that are gaining attention from industry, academia, and governments, i.e., digital twins and data trusts. First, we proposed the use of digital twins (DTs) to generate synthetic records of patient's heart rate data. DTs are virtual replicas of the actual data and were created using two synthetic data generative models - Gaussian Copula (GC) and Tabular Variational Autoencoder (TVAE). The GC and TVAE achieved a maximum data quality score of 88% and 96% respectively. Next, we posit that the DTs should be shared with a data trusts layer. Data trusts are fiduciary frameworks that govern multi-party data sharing. The data trusts enforce access controls (based on metrics such as location, role-based, and policy-based) to the synthetic health data and reports to the data subject. The preliminary evaluations of the work show that merging the two techniques (i.e., synthetic data digital twins and data trusts) enforces better privacy for health data access. The synthetic data ensures more anonymization while the data trusts provide easy auditing, tracking, and efficient reporting to the patient or data subject. The paper also detailed the architectural design of the data trusts and evaluated the efficiency of the access control techniques.