Just to follow up, after I flew the flights, I called both Priceline and LAN (the airline) and they both pointed their fingers to each other as the responsible party and that they would not refund any improperly collected taxes. LAN even said they have never heard of refunding taxes even if I bought directly through them. I appealed to my credit card, and they refused to get involved because the original charge was from too long ago (more than 6 months) even though the flights were recent.