The rapid rise in AI conference submissions has driven increasing exploration of large language models (LLMs) for peer review support. However, LLM-based reviewers often generate superficial, formulaic comments lacking substantive, evidence-grounded feedback. We attribute this to the underutilization of two key components of human reviewing: explicit rubrics and contextual grounding in existing work. To address this, we introduce ReviewBench, a benchmark evaluating review text according to paper-specific rubrics derived from official guidelines, the paper’s content, and human-written reviews. We further propose ReviewGrounder, a rubric-guided, tool-integrated multi-agent framework that decomposes reviewing into drafting and grounding stages, enriching shallow drafts via targeted evidence consolidation. Experiments on ReviewBench show that ReviewGrounder, using a Phi-4-14B-based drafter and a GPT-OSS-120B-based grounding stage, consistently outperforms baselines with substantially stronger/larger backbones (e.g., GPT-4.1 and DeepSeek-R1-670B) in both alignment with human judgments and rubric-based review quality across 8 dimensions. The code is available at https://github.com/EigenTom/ReviewGrounder.