We describe a fundamental problem in fitting rheological data to infer parameters and thus structural information about a material. The results may depend greatly on subjective choices in the fitting method making such inferences non-unique and therefore highly uncertain or wrong. We study experimental data and demonstrate that the most commonly used fitting scheme for oscillatory linear viscoelastic data is deceptively wrong for the purpose of inference, i.e., viscoelastic moduli (G ',G '') weighted by the experimental data. Our results establish best practices for fitting rheological data, linear viscoelastic or otherwise, with strong implications for inverse problems of structural inference.