The decay B0→ψ(2S)K+π− is analyzed using 3  fb−1 of pp collision data collected with the LHCb detector. A model-independent description of the ψ(2S)π mass spectrum is obtained, using as input the Kπ mass spectrum and angular distribution derived directly from data, without requiring a theoretical description of resonance shapes or their interference. The hypothesis that the ψ(2S)π mass spectrum can be described in terms of Kπ reflections alone is rejected with more than 8σ 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.