High-precision 1H(e,e'p)pi(0) measurements at Q2 = 0.126 (GeV/c)2 are reported, which allow the determination of quadrupole amplitudes in the gamma*N-->Delta transition; they simultaneously test the reliability of electroproduction models. The derived quadrupole-to-dipole ( I = 3/2) amplitude ratios, R(SM) = (-6.5+/-0.2(stat+sys)+/-2.5(mod))% and R(EM) = (-2.1+/-0.2(stat+sys)+/-2.0(mod))%, are dominated by model error. Previous R(SM) and R(EM) results should be reconsidered after the model uncertainties associated with the method of their extraction are taken into account.