I'll have to dig out some old info I have, but I believe that there were two Greek army loadings for the 6.5x54mm.

One was for the M1903 etc. rifle/carbine and the other was for an Austrian machine gun that Greece used at the time. I forget the name but I have the info at home in a Greek reference.

I have seen (and may still have) a copy of the box as I translated it for someone.

So maybe the thick rimmed stuff was for the machine gun.

George