The usual argument for automatic ambipolarity of neoclassical panicle fluxes in a tokamak is based on the flux surface averaged toroidal momentum equation. It does not apply when fluctuations are present, because they also contribute to the momentum. In the case of electrostatic fluctuations, their contribution comes from the FLR pressure tensor. The same pressure tensor gives rise to a difference in the drift velocities of ions and electrons, and hence to non-ambipolar anomalous transport. The mean (jxB)j force introduced by magnetic fluctuations can be much larger, as in the associated non-ambipolar particle flux. Any non-ambipolarity in the anomalous transport affects the ambipolar electric field. Because of their high Z, impurity neoclassical transport is most strongly affected. This can explain the pump-out of impurities by MHD activity.