iahphx--just curious whatever happened in ANC.
On Thrifty Blue Chip free days, the 29.11% in taxes in ANC is calculated on the pre-discounted rate, because the "free days" are not considered a discount but are rather "direct billed" to corporate headquarters. Therefore, to the taxing authorities, the rental is charged the normal rate; the only difference is who is "paying" for the rental. As the certificates can only be applied to the base rate, the customer is left responsible for the taxes.
National's free days appear to be an actual discount off of the rate. Whether rentals are taxed pre-discount or post-discount seems to be dependent on the taxing authorities in the location's jurisdiction. In NYC and ANC, the rental appears to be taxed on the final post-discount subtotal. So, if the free day were applied as a discount off of the full rate, you would pay less in taxes; if it were applied as a form of payment (as is the case with Thrifty), you would pay full taxes.
As for Hertz: too late to do anything about it now, I assume, but there is a Hertz downtown that avoids the 11.11% airport surcharge and only charges the 18% city and state taxes. Might be good to know for next time if indeed you were charged full taxes at ANC.