Honestly, I think they realized the Sith Warrior story would have been extremely hollow had they let the JK kill the Emperor hence they came up with that email that cheapens both stories. It would have been better IMO if the Sith Warrior was told of the Emperor's death, but asked to maintain the illusion that he was the Wrath to keep the Dark Council and the Dread Masters in line.
It wasn't just the e-mail. The Sith Warrior himself encounters the emperor's voice on Voss and is commanded to kill him, to free the emperor since the voss voice's body is trapped in a location. This is an entire game event and interactive scene long before the post game e-mail.
From that point the gaps would suggest the emperor inhabits another voice, but the lore suggests it takes the emperor time to adapt to a new voice, that would lend itself to the JK killing the emperor's voice since he may even be in a weakened state.