Besides "secret" knowledge like the know-how at jobs, there's things like unwritten social etiquette (especially as it varies from place to place) or interfacing with physical world – reading about chopping tomatoes is different from experience acquired by actually chopping tomatoes.

It isn't. I constantly have access to non-public information, like the life of my peers and corporate secrets. Is it useful or essential or even desirable for LLM products? Hardly not, but it exists.

Edit: for "not in the training data" yes, humans generally can't know what they can't know.