The use of Conversational Generative Artificial Intelligence (GenAI) is growing as a way to interact with health information, especially for the public. This theory-based conceptual synthesis suggests a multilevel governance approach to reducing the likelihood for generated information to become unsafe action – GenAI health information resilience (GenAI-HIR). Its contribution is immediately usable and practical — deploying organizations and public-health actors and public-health actors can use the consequence-based control tiers, actor-specific safeguards, and domain-level audit anchors, and the proposed competency configuration still needs to be validated and is a research agenda for the future. Five conceptually distinct functions at the individual and workforce levels describe at which point protection may contribute to the decision pathway, but are not necessarily assumed to be empirically separable: recognize, interrogate, verify, contextualize, and escalate. Organizational capacity is limited to controls particular to created health information such as authorized sources, attainable human routing, incident monitoring and corrective action. Platform and regulatory conditions are constraints, safety, access, calibrated trust, and equity, outcomes. The framework was created using an expert guided purposive synthesis of the 62 sources that were retained, not a systematic review process. It distinguishes between an explanatory risk model and a normative control architecture and categorizes outputs with respect to type of output, severity, urgency, reversibility, context dependence, mitigation feasibility, and remaining risk. Falsification criteria are now included in six propositions. The candidate self-report indicators are kept as material for the cognitive interviewing only and must be correlated with behavioral vignettes before use for psychometric purposes. GenAI-HIR is therefore not a validated scale, certification standard or replacement for accessible professional care; it is a model for competency that can be falsified in future research and a governance structure that can be audited for current implementation.