Rick:
OE taxes can be calculated on 1 of 2 bases: Line-by-Line or Invoice Total. In the first case, tax is calculated on each line and then added together at the end. In the second case, taxes are calculated only on the pre-tax total. Using the first method I have seen cases where the tax appears wrong by a penny or two when compared to the pre-tax total. It's not wrong, just different based on rounding (or absence of rounding).
The factors that make this difference apparent are number of lines on the invoice, dollar amounts and tax rates. For instance, an invoice with 1 line and an even dollar amount (ie. $100) is always going to have the same tax amount regardless of the selected method. The tax rate(s) also matter. For instance, a 5% tax usually has the same calculation regardless of the method selected. However a 7% tax (which doesn't divide into 100 evenly) can result in a total tax figure which varies depending on the method selected.
The setting is contained in the OE Company Profile on the "System Options" tab. Look for "Calculate tax amount by".
Try changing the setting and trying your tests again.
Having said all of that, I wouldn't expect that the Data Integrity Check would find a problem. Nor can I see why IC 8.1C would make a difference. Has a tax rate changed lately? Please let us know your results.