Hi Scott,
As I already wrote, the user has made a purchase with a valid VAT number and has checked the exempt VAT checkbox and the price paid during the order is VAT exempt. So the front end transaction is correct.
However, in the manage order detail page, the VAT rate is added to the total price (so the displayed total amount is different from the price paid by the user). In the 'Invoice Info' tab, the VAT number is stored and the VAT exempt is checked.
As the VAT is added to the price, if the admin resend the email, the user will not receive the price originally paid, so it is inconsistent.
Note that in the 'Invoice Info' tab, the VAT number can be real-time validated and the VAT exempt checkbox is editable, but, as you have mentioned, checking or unchecking it does not "recalc the order with tax exemption after an order is already placed".
So even if it does not recalculate, the VAT rate & amount at the bottom of the manage order detail page should be 0 if the user was not charged VAT when purchasing its products.