Watermarking is not at all like a digital signature and a lot like steganography. I only have a surface level understanding of the process, but it works by biasing token selection to encode information into the resulting text in a way that's resistant to later modifications and rephrasing.
I have my doubts about the effectiveness of this method and realistically, it won't make any difference because the bad actors will just use an LLM that doesn't snitch on them, so you're technically correct.