Lets do a thought exercise:

You are stranded in a desert island. You start writing a message "Help, I am..." and pass at that point.

Somebody finds the message. They can no doubt come up with plausible continuations like "Help, I am Robinson Crusoe" or "Help, I am hungry" but they cannot create information. No matter how smart and how long you stare at the message, that is not going to tell you what the original person would have written.

Isn't it from Claude Shannon that information lowers uncertainty? Infinite regurgitation or massaging of data does not create new information. You will get the information form the LLM, not from that original person.