Open-generation bias benchmarks evaluate social biases in Large Language Models (LLMs) by analyzing their outputs. However, the classifiers used in analysis often have inherent biases, leading to unfair conclusions. This study examines such biases in open-generation benchmarks like BOLD and SAGED. Using the MGSD dataset, we conduct two experiments. The first uses counterfactuals to measure prediction variations across demographic groups by altering stereotype-related prefixes. The second applies explainability tools (SHAP) to validate that the observed biases stem from these counterfactuals. Results reveal unequal treatment of demographic descriptors, calling for more robust bias metric models.