He performed at an average level when number series were presented forward (five digits; 50th percentile), but exhibited above average skills when he was asked to recite them backwards (four digits; 91st percentile)
Should I have him correct the narrative as well as the scoring? He's been very resistant to any of our questions about the scores so I'm trying to put together the appropriate data to give him.
I know testing for giftedness can be very expensive and the fact that you received an incorrect score and little to no explanation of your child's performance strikes me as rather repugnant.
About your son's performance on digit span: forward digit span only has a g-loading of about 0.30, while reverse digit-span has a g-loading of about 0.40. This difference of 0.1 seems rather small, but in fact 77% more g enters into the reverse digit-span task than it does in the forward digit-span task. Thus, your son's much superior performance on reverse digit-span is to be expected. Moreover, there are many gifted children whose performance on forward digit span scarcely exceeds the population mean, and a number of them even perform in the below average range on this task. Thus, your son's performance is nothing to worry about.
