Yes, language is like that, at least the kind of language produced by LLMs. All LLMs produce a probability distribution at each token. If you run the LLM multiple times with the same prompt you will observe it generate different responses. Using the watermarked prng does not change the distribution.
When generating tokens that might be critical to the tone or grammar or correctness, the probability distribution might be 99% on a certain token. In these cases, with or without watermarking, the output will almost always be that same token. E.g., if you ask "please output the exact word watermelon", the LLM will output watermelon with 99%+ probability even with watermark (i.e., the output won't actually be detectable as watermarked).
When generating tokens that might be critical to the tone or grammar or correctness, the probability distribution might be 99% on a certain token. In these cases, with or without watermarking, the output will almost always be that same token. E.g., if you ask "please output the exact word watermelon", the LLM will output watermelon with 99%+ probability even with watermark (i.e., the output won't actually be detectable as watermarked).