The decay B-0 -> psi(2S)K+pi(-) is analyzed using 3 fb(-1) of pp collision data collected with the LHCb detector. A model-independent description of the psi(2S)pi mass spectrum is obtained, using as input the K pi mass spectrum and angular distribution derived directly from data, without requiring a theoretical description of resonance shapes or their interference. The hypothesis that the psi(2S)pi mass spectrum can be described in terms of K pi reflections alone is rejected with more than 8 sigma significance. This provides confirmation, in a model-independent way, of the need for an additional resonant component in the mass region of the Z(4430)(-) exotic state.