The destination of the beer run is likely important. Was it a local store, a brewery, or some other place? Also, the time and circumstances around the run. For example, if it was during a special event or a difficult time in the community.
I'm not sure specifically which 'the last beer run true story' you are referring to. It could be about a final trip to get beer that had some interesting or memorable events. Maybe it was a group of friends' last adventure to fetch beer before a big change in their lives.