As far as Fox, my understanding is that his data was statistically driven while Dyer was a mental prodegy who memorized every Union regiment's statistics. Both have distinct value but may not be accurate when compared to each other.
The math error may or may not have been "discovered" but the question of loyalty and courage were embraced as a "provable" topic by several authors, Dyer's, Fox and Livermore and more modern authors all developed methodologies to prove courage on the part of both Union and Confederate regiments. Fox specifically used casualties as a definition of courage and makes for some interesting reading. States whose regiments show up in Fox adopted these theories in a competitive way. That is why Minnesota claims to have the first Union volunteer, or Kansas says that they had the highest participation per capita rate, or Vermont troops were among the bravest, etc. While making for interesting speculation it doesn't change the fact that both Union and Confederate regiments for the most part were ill prepared or underarmed to assume warfare with each other and, yet, did so.
For me the disappointment is the lack of accurate records, but it also makes discovery that much more interesting.