It seems possible, in fact reasonable, to understand my observation as following from your assumed "correlation". I gave it context that it is having a conversation with an expert, it correlates it's output with the context. A non-expert user can't fake that context so they never see similar correlated output. This context-correlation doesn't happen if one uses "You are a expert ..." prompting "tricks".

My experience has been, if you speak like an expert who is speaking to an expert you get better results. I'm not sure how that is anthropomorphizing. It is just "if I do these things, I get these results".