I had this problem with a brand new set of sachs cranks and supposedly matching sealed BB unit. I solved it by "Skimming" the face of the cup with a file. It took awhile but I did not need to remove much material. The result looked really neat as the cup and crank looked if they were one piece.
I do remember sheering off the face of a Stronglight fixed cup once when I first started cycling. I pushed my self along about 5 miles with a stick I picked up at the side of the road. i did not want to pedal in case I wrecked the axle too. Being able to afford just a new cup was already an issue!
Regards
Martin Coopland, in a cool Scotland.