Watermarking for large language models (LLMs) embeds a statistical signal during generation to enable detection of model-produced text. While watermarking has proven effective in benign settings, its robustness under adversarial evasion remains contested. To advance a rigorous understanding and evaluation of such vulnerabilities, we propose the \emph{Bias-Inversion Rewriting Attack} (BIRA), which is theoretically motivated and model-agnostic. BIRA weakens the watermark signal by suppressing the logits of likely watermarked tokens during LLM-based rewriting, without any knowledge of the underlying watermarking scheme. Across recent watermarking methods, BIRA achieves over 99\% evasion while preserving the semantic content of the original text. Beyond demonstrating an attack, our results reveal a systematic vulnerability, emphasizing the need for stress testing and robust defenses.