This is more about the rental car terminal than about Budget operations. My daughter's experience while I waited for her to complete her Budget reservation seemed fine, however.
PHX has solved the ugly step-child situation that car rental operations cause for most airports. Cram the check-in desks into the farthest corner of baggage pickup? Send rental car clients out into the weather, or into funky garages to get their car as well grease monkey attitudes? Not at PHX.
There are air conditioned coaches dedicated to rental car customers that stop at each airline terminal. Drivers will actually help you board as well as help to board unwieldly luggage. PHX has an entire terminal dedicated to rental car agencies. It's about five miles away from the international PHX, but worth the ride. You can qeue in whichever agency's lines you choose. Each rental agency has their own three walls.
After the endless paperwork, you exit the sparkling concourse, visit a booth in the contiguous garage, and walk to a parked car.
If you don't have the correct paperwork, and/or are unwilling to show ID aong with the docs, a weathered, uniformed clerk in another booth is authorized to throw the switch on reverse tire spikes in the exit lane. That's rental car border protection at its finest..