I think you've confused some things. Pay careful note to what I'm calling a distribution. There are many distributions at play here but I'm referring to two specific ones that are clear from context.

I think you've also made a leap in logic. The jury's still out on whether LLMs have internalized some world model or not. It's quite difficult to distinguish memorization from generalization. It's impossible to do when the "test set" is spoiled.

You also need to remember that we train for certain attributes. Does the LLM actually have introspection or does it just appear that way because that's how it was optimized (which we definitely optimize it for that). Is there a difference? The duck test only lets us conclude something is probably a duck, not that it isn't a sophisticated animatronic that we just can't distinguish but someone or something else could.