The literature on trust in large-language-model (LLM) outputs has clustered around four points of intervention: model-level alignment, input-shaping at prompt time, generation-time decoding constraints, and post-hoc output verification. We argue that a fifth, distinct category, workflow-level trust infrastructure, has been recognized in practice but underspecified in theory. Drawing on two production agentic-AI systems for public-interest data production, we formalize "auditable by construction" as a property of pipeline structure rather than model output, and propose a reference architecture in which typed stage contracts, convergence-based stopping criteria, ontology-anchored normalization, authoritative-data reconciliation, and first-class provenance combine to produce statistical-grade outputs. We demonstrate the approach with case studies of two deployed systems: multi-agent technology supply-chain analysis and multi-agent reconciliation of classified U.S. intelligence budgets. We then map the resulting pattern onto established official-statistics frameworks (Total Survey Error; the Generic Statistical Business Process Model).