The brightness temperature difference product that can be used to infer the presence of fog/low clouds exploits emissivity differences in water clouds at 3.9 micrometers vs. 11 micrometers.  When the two bands have a co-registration error, as documented here, however, a false signal can arise.  A benefit of using a fused product is that the false signal is checked against a cloud mask and model data so that false positives can be identified and ignored.