Dark Souls Remastered | Ornstein and Smough boss fight on NG+1 with two summoned phantoms (players)

Both of the players I summoned were part of the Warrior of Sunlight covenant. I otherwise don't think that a Sunlight Medal normally drops unless the player who is awarded it beat this boss fight as a phantom summoned to someone else's realm and a member of that covenant. If I'm wrong, someone please tell me.

Drops:

150,000 souls
1x Soul of Smough
1x Humanity
1x Sunlight Medal