The rapid proliferation of AI-generated video necessitates robust detection tools that offer both high accuracy and human-interpretable explanations. While existing MLLM-based detectors rely on supervised fine-tuning (SFT) or direct preference optimization (DPO), these methods are often bottlenecked by static, pre-labeled datasets that fail to capture the evolving, multi-step physical inconsistencies of modern generative models. To bridge this gap, we introduce VidGuard-R1, the first video authenticity detector to utilize group relative policy optimization (GRPO). Moving beyond passive preference matching, VidGuard-R1 employs a reinforcement learning framework that encourages the model to explore and rank multiple reasoning paths. By introducing specialized reward models for temporal stability and diffusion-aware complexity, we incentivize the model to discover 'physics-grounded' artifacts. Our contributions include: (1) a curated dataset of 140,000 challenging real/fake video pairs; (2) a GRPO-based training paradigm that achieves state-of-the-art zero-shot performance; and (3) a reasoning-first architecture that provides precise, verifiable rationales for its forensic judgments. Project website: https://vidguard-r1.github.io/.