I don't know exactly what type of sling the originals had, but I think the Pedersolis could have a sling with a standard style loop on one end and a strand tie style on the barrel end.
I guess that could be useful if a sling is allowed in the back position as you could slide the sling down the barrel if needed. Good question though. I have wondered the same since the match rifles have the swivel in front of the trigger guard but the African Hunter has the eyelet but not the swivel.