Priceline isn't a traditional 3rd party in this case, they are only making the reservation. You still deal with the rental company directly. I've changed my rental for early October twice today using Autoslash through Priceline, once to Alamo then again to Budget, in both cases I could see my rental with my loyalty number attached on both company websites within 5 minutes, same as if you booked through Costco, AAA or most any other option. Almost all of the 3rd party problems are when you pay the 3rd party who then pays the provider.