I don't think this is a good argument. There exist digital watermarking techniques for image and video that are imperceptible to humans but still survive cropping, rotation, resizing, recompression, or an analog round trip (photographing the image or pointing a camera at the video). These watermarks aren't, like, hiding in the low-bits of color information, they're spread among many perceptible details.

It's not clear to me that it's impossible, or even especially difficult, to make something that survives a casual LLM paraphrase. Remember, all you need to encode is a single bit of info. There's a lot of space to redundantly encode that signal.