Large distributed systems are now operated through layers of schedulers, container controllers, service meshes, monitoring pipelines, and human runbooks. These mechanisms improve scale, but they also create governance problems: local controllers can fight one another, remediation rules may violate service-level or compliance constraints, and operators often lack a compact record of why a system changed. This paper presents Policy-Bounded Agent Governance (PBAG), a 2021-era architecture for coordinating intelligent software agents that monitor, diagnose, and repair distributed systems while remaining subject to explicit operational authority. PBAG combines local agents near services and clusters with a governance plane that checks action rights, conflict constraints, freshness requirements, and audit completeness before any adaptation is committed. The method builds on autonomic computing, agent-based software engineering, self-adaptive architecture, cluster management, cloud elasticity, and machine-learning systems practice. A controlled prototype study evaluates PBAG across four operational scenarios: load surge, replica degradation, stale forecasting input, and accelerator-backed training contention. Compared with manual runbooks and independent local agents, PBAG reduces median recovery time by 37%, lowers conflicting actions from 18 to 4 per 120 incidents, and keeps p95 request latency within 7% of a static-policy baseline. The central result is that intelligent agents are most useful for distributed-system governance when their autonomy is bounded by shared policy, explicit conflict resolution, and durable decision records.