The venue only needs a PEL licence, PRS cannot collect royalties on behalf of non PRS members but can collect royalties for material belonging to their members. The responsibility of submitting set list details is that of the venue or promoter. If works are only performed that have no conection to PRS then the set list submission needs to point this out to pRS.
All the while the PRS database is a total shambles and they do try to collect for works not belonging to them if you let them get away with it, the rules for arrangements are totally disregarded by PRS and also the rules for logging of those arrangements are not adhered to, thus you find many artists with the self same work registered on the database. PRS also claim for works not registered on their database and claim that this fact is irrelevant, I think it is anything but irrelevant as how then do they know who the material belongs to and more importantly who to make royaly payments to for the performance.