I'm not sure I follow you. I didn't get the impression that Marken's model had more tunable parameters than there were data points under study, or that it actually was tunable in such a way as to create any desired result.

In the section "Quantitative Validation", under Table 1, it says (italics mine):

The model was fit to the data in Table 1 by adjusting only the speed parameter, s, for each prescription component control system... The results in Table 1 show that the distribution of error types produced by the model corresponds almost exactly to the empirical distribution of these rates. The values of s that produced these results were 0.000684, 0.000669, 0.000731 and 0.000738 for the Drug, Dosage, Route and Other component writing control systems, respectively.

As you vary each speed component within the model, the fraction of errors by that component varies all the way from 0 to 1, rather independently of each other. Thus for any empirical or made-up distribution of the four error types, Marken would have calculated values for his four parameters that caused the model to match the four data points; so despite his claims, the empirical data offer literally zero evidence in favor of his model. Ditto with his claim that his model predicts the overall error rate.

I'll get to the rest of this later.