Your at the death of the Lich King and you see the helmet on the floor next to frostmourne. You see Fordring pick it up, now here are two options:
1. Would you take it out of his hand and destroy it or;
2. Would you let him crown Bolvar the new Lich King?
This has nothing to do with a lore point of view.
Yes, if option 1 was picked, the scourge would go crazy, but you have already killed all the bosses in Naxxaramas and Icecrown Citadel, so most of the scourge generals are dead. Scholo and Strat have also been taken down.