I have a feeling including a parenthetical like that would invite more confusion than it avoids. "Oh cool, I guess my magical ESP powers are just one of the unlikely cases where I can be correlated with the hidden coin flips without any causal influence."

Because "correlation" is normally taken to mean a systematic effect that can be expected to be predictive of future samples, or something. In this specific case, Pearl probably means something more precise by it (like correlations between nodes in a particular causal model).

I suppose you could accurately clarify the original quote by saying "systematic correlation", which would pin down the idea referred to for people who haven't read the book.