Leyline of the Void and exiling stolen permanents
He's right. It goes directly to his graveyard.



Just to be clear, he controls Leyline of the Void, which has the following ability:


  If a card would be put into an opponent's graveyard from anywhere, exile it instead.


You control one of his creature, which you somehow sacrifice.


  701.14a To sacrifice a permanent, its controller moves it from the battlefield directly to its owner’s graveyard. [...]
  
  108.3. The owner of a card in the game is the player who started the game with it in his or her deck. [...]


As part of sacrificing the creature, you place it in his graveyard. The Leyline's replacement effect does not apply since the creature enters his graveyard (being the creature's owner), not the graveyard of one of his opponents.



As for whether you benefit from the sacrifice, the answer isn't clear, since it's not clear what you mean by that.


If sacrifice is part of the cost of activating an ability: The ability resolves as normal, no matter where the creature ends up. As the person who activated the ability, you control it.
If the creature has an ability that triggers on leaving the battlefield, it would trigger with you as the controller of the ability. (LTB abilities look at the state of the game before the event happen.)
If another one of your permanents has an ability that triggers whenever you sacrifice a creature, it triggers no matter where the creature ends up. The sacrifice action still take places even if the effect of sacrifice is modified by a replacement effect. 
If another one of your permanents has an ability that triggers whenever a creature enters your graveyard, it will not trigger since the creature moved from the battlefield to his graveyard.
If the creature has an ability that triggers when it enters a graveyard, it will trigger with your opponent as the controller since it went to his graveyard.