The condition that the ETH imposes on the diagonal elements of an observable is responsible for the equality of the predictions of the diagonal and microcanonical ensembles. However, the equality of these long-time averages does not guarantee that the fluctuations in time around this average will be small. That is, the equality of the long-time averages does not ensure that the expectation value of A ^ ^ will settle down to this long-time average value, and then stay there for most times.