From my background in environmental analyses, as a regulatory auditor, I'm a dog for calculations. I've seen too many times that lab's can "hide" fraud in their data, and we've found it through verification of the calculations.
The EPA methods often define the response factor (or relative response factor, or calibration factor) as response divided by concentration (or R/C). Response can be either area or height. But I've also seen, as you discussed, that some software quantitates RF as C/R (Thermo Target software).
The primary concern with this is that some EPA methods (8260B and 8270C, and CLP methods) have minimum reponse factor requirements based on R/C. Obviously, if the software quants C/R, then we end up comparing apples with oranges, and the lab really isn't evaluating the data appropriately. And the data may not meet the method requirements.
I just make sure that the lab's SOP clearly states the software's equations all the way to the final calculation of concentration that the lab will report, and that they've addressed any minimum RF issues.