I was under the impression that without also forcing the exact seed (which is randomly chosen and usually obfuscated), even providing the same exact prompt is unlikely to provide the same exact summary. In other words, under normal circumstances you can't even prove that a prompt and response are linked.
I'm under the impression that seed only effects anything if temperature > 0. Or more specifically that the LLM given a sequence of input tokens deterministically outputs the probability for each possible next token, and then the only source of randomness is in the procedure for selecting which of those next tokens to use. And that temperature = 0 means the procedure is "select the most likely one" with no randomness at all.
The seed and the actual randomness is a property of the inferencing infrastructure, not the LLM. The LLM outputs probabilities, essentially.
The paper is not claiming that you can take a dump of ChatGPT responses over the network and figure out what prompts were given. It's much more about a property of the LLM internally.