The autonomy and contextual complexity of LLM-based agents render traditional access control (AC) mechanisms insufficient. Static, rule-based systems designed for predictable environments are fundamentally ill-equipped to manage the dynamic information flows inherent in agentic interactions. This position paper argues for a paradigm shift from binary access control to a more sophisticated model of information governance, positing that the core challenge is not merely about permission, but about governing the flow of information. We introduce Agent Access Control (AAC), a novel framework that reframes AC as a dynamic, context-aware process of information flow governance. AAC operates on two core modules: (1) multi-dimensional contextual evaluation, which assesses not just identity but also relationships, scenarios, and norms; and (2) adaptive response formulation, which moves beyond simple allow/deny decisions to shape information through redaction, summarization, and paraphrasing. This vision, powered by a dedicated AC reasoning engine, aims to bridge the gap between human-like nuanced judgment and scalable Al safety, proposing a new conceptual lens for future research in trustworthy agent design.