Assuming that light neutrino masses are described by the Weinberg operator and constrained by a flavour symmetry, we identify all flavour groups and representations providing an approximate description of lepton masses and mixings in the symmetric limit. It turns out that the neutrinos are always either anarchical or have an inverted hierarchical spectrum. We then investigate whether the flavour theory predictions obtained within the Weinberg operator description are equivalent to those obtained within the full UV theory, using type I see-saw as a prototypical example. That is not always the case, and the conditions for the equivalence are found. If the hint of a normal hierarchical neutrino spectrum were confirmed, we would then conclude that either the symmetry breaking effects play a primary role in the understanding of neutrino flavour observables, or the UV flavour theory does not provide the same predictions as the effective one.