High-precision H(e,e'p)pi0 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 amplitude ratios, Rsm=(-6.5 +- 0.2{stat+sys} +- 2.5{mod}) % and Rem=(-2.1 +- 0.2{stat+sys} +- 2.0{mod}) %, are dominated by model error. Previous Rsm and Rem results should be reconsidered after the model uncertainties associated with the method of their extraction are taken into account.