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.**)