Retrieval-Augmented Generation (RAG) enhances Large Language Models by grounding their outputs in external documents. These systems, however, remain vulnerable to attacks on the retrieval corpus, such as prompt injection. RAG-based search systems (e.g., Google's Search AI Overview) present an interesting setting for studying and protecting against such threats, as defense algorithms can benefit from built-in reliability signals -- like document ranking -- and represent a non-LLM challenge for the adversary due to decades of work to thwart SEO. Motivated by, but not limited to, this scenario, this work introduces ReliabilityRAG, a framework for adversarial robustness that explicitly leverages reliability information of retrieved documents. Our first contribution adopts a graph-theoretic perspective to identify a "consistent majority" among retrieved documents to filter out malicious ones. We introduce a novel algorithm based on finding a Maximum Independent Set (MIS) on a document graph where edges encode contradiction. Our MIS variant explicitly prioritizes higher-reliability documents and provides provable robustness guarantees against bounded adversarial corruption under natural assumptions. Recognizing the computational cost of exact MIS for large retrieval sets, our second contribution is a scalable weighted sample and aggregate framework. It explicitly utilizes reliability information, preserving some robustness guarantees while efficiently handling many documents. We present empirical results showing ReliabilityRAG provides superior robustness against adversarial attacks compared to prior methods, maintains high benign accuracy, and excels in long-form generation tasks where prior robustness-focused methods struggled. Our work is a significant step towards more effective, provably robust defenses against retrieved corpus corruption in RAG.