Generative AI systems now mediate newsfeeds, search rankings, and creative content for hundreds of millions of users, positioning a handful of private firms as de-facto arbiters of truth. Drawing on a comparative-historical lens, this article juxtaposes the Galileo Affair, a touchstone of clerical knowledge control, with contemporary Big-Tech content moderation. We integrate Foucault's power/knowledge thesis, Weber's authority types (extended to a rational-technical and emerging agentic-technical modality), and Floridi's Dataism to analyze five recurrent dimensions: disciplinary power, authority modality, data pluralism, trust versus reliance, and resistance pathways. Primary sources (Inquisition records; platform transparency reports) and recent empirical studies on AI trust provide the evidentiary base. Findings show strong structural convergences: highly centralized gatekeeping, legitimacy claims couched in transcendent principles, and systematic exclusion of marginal voices. Divergences lie in temporal velocity, global scale, and the widening gap between public reliance and trust in AI systems. Ethical challenges cluster around algorithmic opacity, linguistic inequity, bias feedback loops, and synthetic misinformation. We propose a four-pillar governance blueprint: (1) a mandatory international model-registry with versioned policy logs, (2) representation quotas and regional observatories to de-center English-language hegemony, (3) mass critical-AI literacy initiatives, and (4) public-private support for community-led data trusts. Taken together, these measures aim to narrow the trust-reliance gap and prevent GenAI from hardcoding a twenty-first-century digital orthodoxy.