The data sample of Lambda(0)(b) -> J/psi pK(-) decays acquired with the LHCb detector from 7 and 8 TeV pp collisions, corresponding to an integrated luminosity of 3 fb(-1), is inspected for the presence of J/psi p or J/psi K- contributions with minimal assumptions about K(-)p contributions. It is demonstrated at more than nine standard deviations that Lambda(0)(b) -> J/psi pK(-) decays cannot be described with K- p contributions alone, and that J/psi K- contributions play a dominant role in this incompatibility. These model-independent results support the previously obtained model-dependent evidence for P-c(+)-> J/psi p charmonium-pentaquark states in the same data sample.