AI technologies are becoming a fundamental element of healthcare information systems in areas of diagnostic imaging, predictive analytics, telemedicine, and continuous patient monitoring. Nevertheless, AI adoption has moved ahead of privacy protections, security architectures, and governance structures that would allow maintaining trust among stakeholders. This systematic review combines a broader collection of relevant core studies and their supporting literature (2015-2026), including conceptual reviews, expert-derived frameworks, AI-scenario experiments, security case syntheses, and analysis of legislations, to summarize what is known about the establishment of digital trust in healthcare with AI. Several main themes can be derived from the study. First, regardless of the methodology, all the core studies are unanimous about the socio-technic nature of trust emerging through the interrelationship between technological security measures, organizational governance, and human factors. Second, privacy is recognized as the major challenge to AI implementation, and the regulatory baseline for trust frameworks is incomplete because there is no statutory basis to address many aspects of contemporary AI healthcare in instruments such as HIPAA and it differs from one jurisdiction to another. Third, explainability serves as the precondition of trust but becomes the most recommended yet the least proven solution, thus leaving open the borders of allowable clinical automation. Overall, the review highlights a structural contradiction: while there is much enthusiasm about adoption and effectiveness of the technology, primary sources confirm the fragmentation of governance at the state level and the decreasing public confidence. The main message is that validation is needed: few of the frameworks discussed have been experimentally verified in a deployed clinical system; there is no standard psychometric tool to measure the trust generated by frameworks; and finally, patients as the bearers of trust have not been studied.