This talk reframes “trustworthy GenAI” as a problem of legitimacy in sociotechnical systems. It argues that data—how it is curated, ranked, retrieved, and labeled—now functions as a governance mechanism that redistributes visibility and voice. Using cases from GEO (Generative Engine Optimization) and platform provenance policies, we show how “evidence design” (tables, comparisons, citations), RAG/retrieval rules, and interface signals (sponsored tags, uncertainty cues, timestamps) authorize some claims while marginalizing others. Trust is treated as relational and performative: produced through public rituals of disclosure, correction, and contestation rather than through engineering alone. We outline a social-science toolkit—exposure audits, credibility experiments, discourse analysis, and participatory methods—to study whose knowledge is surfaced and believed. It closes with a normative and practical framework: legitimacy, accountability, contestability, and care (LACC), plus operational metrics (evidence diversity, provenance coverage, correction latency) that communicators, platforms, and regulators can use to align GenAI-mediated communication with public confidence and data justice.