It's the attention mechanism at work, along with a fair bit of Internet one-up-manship. The LLM has ingested all of the text on the Internet, as well as Github code repositories, pull requests, StackOverflow posts, code reviews, mailing lists, etc. In a number of those content sources, there will be people saying "Actually, if you go into the details of..." or "If you look at the intricacies of the problem" or "If you understood the problem deeply" followed by a very deep, expert-level explication of exactly what you should've done differently. You want the model to use the code in the correction, not the one in the original StackOverflow question.
Same reason that "Pretend you are an MIT professor" or "You are a leading Python expert" or similar works in prompts. It tells the model to pay attention to the part of the corpus that has those terms, weighting them more highly than all the other programming samples that it's run across.
This is such a good explanation. Thanks
Of course I can't be certain, but I think the "mixture of experts" design plays into it too. Metaphorically, there's a mid-level manager who looks at your prompt and tries to decide which experts it should be sent to. If he thinks you won't notice, he saves money by sending it to the undergraduate intern.
Just a theory.