If the connection between the fundamental theory and neutrino mass matrices M_ u is sufficiently complicated all traces of underlying symmetries might be erased and an 'anarchical' M_ u, with random entries, can arise. It has been claimed that such random matrices generically prefer large mixing making unnecessary to invoke flavour symmetries to explain the observed pattern of neutrino mixing angles. A critical analysis of this idea (paying particular attention to the role of unphysical phases and coordinate dependence) shows that basis-independent, random M_nu's are not biased towards large values of the neutrino mixing angles, contrary to previous claims. As a result, the case for anarchy in the neutrino sector is considerably weakened.