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The reliability of VLM-as-a-Judge is critical for the automatic evaluation of vision-language models (VLMs). Despite recent progress, our analysis reveals that VLM-as-a-Judge often pays limited attention to the image when making decisions. Instead, they often blindly favor the more informative answer, even when they can recognize it conflicts with the image content. We call this problem informativeness bias, which significantly undermines judge reliability. To address it, we propose BIRCH (Balanced Informativeness and CoRrectness with a Truthful AnCHor), a judging paradigm that first corrects inconsistencies with the image content in candidate answers, and then compares the answers against this corrected version. This shifts the judge's focus from informativeness to image-grounded correctness. Experiments on multiple models and benchmarks show that BIRCH reduces informativeness bias by up to 17%, resulting in performance gains of up to 9.8%. Our work reveals an overlooked but fundamental flaw in current VLM-as-a-Judge systems and highlights the need for more principled designs.