I have never operated into BHM or on an A300-600, but in my mind the following might be a possible explanation for what happened.
The crew elects to do a GPS approach onto RW18. It is a long evening and both crew members are tired, so instead of using the GPS approach charts take out the LOC charts for RW18 by mistake.
As can be seen on the AVhelard website:
Crash: UPS A306 at Birmingham on Aug 14th 2013, contacted trees and touched down outside airport
There is a 1.3nm offset between the distance to the threshold depending which chart you are using. If the VNAV equivalent on the A300-600 is as poor as some older aircraft I have flown, then they elect to fly the vertical profile in the equivalent of V/S. During the whole approach they are low by the equivalent of 1.3nm. The crew think they are doing fine when they break cloud and they can see the runway lights ahead as well as a few sporadic lights around. The only thing that does not look right are the four reds on the PAPI's. However their calculations show them to be right on profile and the black hole effect makes them feel like they are on profile. They continue the approach in spite of the uneasy feelings they have about the PAPI's. While they discuss what is wrong with the airport systems they are unable to see the dangers that lurk around them. Before they can do anything else they have hit some trees/powerlines and it's game over.