As discussed in chianti-atomic/chianti-idl#12, the Fontes calculation is not actually used in the CHIANTI IDL calculation of the direct ionization cross-section. Rather, all direct ionization cross-sections are computed from the scaled cross sections a la Dere (2007). Is there a reason that the Fontes cross-sections are implemented separately here? @pryoung points out in that issue that the Fontes results were used in producing the fits to the H- and He-like ions.
In the process of doing these comparisons in fiasco in wtbarnes/fiasco#360, where I also implement the Fontes cross-section calculation separately, I find significant differences in all of the ionization rates compared to those results from IDL, but especially in the H- and He-like ions (>10%) where the Fontes cross-section is used. Removing this calculation brings the two results into closer agreement (<10%) though there are still other inconsistencies to be worked out.