I'm not sure what Nad is wondering about, but here's a guess.
She might be puzzled that we're calling
$$ \langle A B \rangle - \langle A \rangle \langle B \rangle $$
the covariance between $A$ and $B$. She might be more used to
$$ \langle A - \langle A \rangle \rangle \; \langle B - \langle B \rangle \rangle $$
However, these are equal! (Fun exercise.)
(**Edit: there was a typo here.**)