There's no difference between those two things. The distribution that matters is the distribution of tokens that are picked not the distribution of tokens the LLM model passed to the selector.
On average the distribution of selected watermarked tokens is the same as the original distribution. You can test this experimentally.
I think there is a possible weakness in the context of the watermarker but that is not your claim iiuc.
On average the distribution of selected watermarked tokens is the same as the original distribution. You can test this experimentally.
I think there is a possible weakness in the context of the watermarker but that is not your claim iiuc.