We present arguments indicating that in presence of friction there is no anomalous scalings in the velocity correlations in the direct cascade in two dimensional turbulent systems. We also suggest that recent experimental observations of the direct enstrophy cascade are governed by a small parameter equal to the ratio of the enstrophy transfer rate over the enstrophy injection rate. The quasi-symmetry of the observed probability distribution functions of the velocity differences is linked to the smallness of this parameter. At leading order in the approximation consisting in neglecting odd order correlations in front of even order ones, the velocity statistics is gaussian with a normal scaling.