Fitting plasma models to high-quality spectra is a crucial tool for deriving diagnostics about the physical conditions in various astrophysical sources. Despite decades of model development, this prescription often provides an unsatisfying description of observational data. We explore some of the origins of the failure of fits of photoionized plasma models to high-resolution X-ray spectra. In particular, we test whether systematic uncertainties in underlying atomic data can account for data model discrepancies, and whether including model uncertainties during spectral fitting can provide statistically acceptable fits and reasonable parameter estimates. We fit Chandra/HETG spectra of NGC 3783 with the photoionized absorber model warmabs. We use the remaining data model discrepancies to estimate the systematic uncertainties of bound–bound radiative rates for individual transitions quantitatively. We then include these uncertainties into warmabs to return a total model uncertainty. We find residual data model discrepancies which are due to systematic errors that cannot be accounted for solely by a modification of the optical depth of strong absorption lines. Furthermore, statistical uncertainties still dominate the fit statistics. The relevance of model uncertainties in spectral fitting will vary on a case-by-case basis. However, they are likely to have a minor effect on most of the currently existing data sets. We conclude that while the quality of atomic data does have an effect on fitting photoionization models, and so demands further improvement, uncertainties in radiative rates cannot be held solely responsible for statistically unacceptable fits. Other sources of systematic uncertainties are likely to be of comparable importance and require further investigation.