The rulings of Graveyard Busybody include:
Cards owned by your opponents still go to the appropriate graveyard.
Speaking of [another ruling], cards in graveyards are shuffled into their owners’ libraries. You won’t put any cards from graveyards you stole, er . . . borrowed into your library.
which appears to imply that the graveyards are "yours", but you don't own the cards.
Which matches how the "owner" in game terms closely shadows the actual owner of the cards, e.g. if a player leaves a multiplayer game, cards they own also leave the game. Which they would do in any case if the player decided to pick up their belongings and go.
(108.3 does say that "Legal ownership of a card in the game is irrelevant to the game rules except for the rules for ante." and that instead "The owner of a card in the game is the player who started the game with it in their deck [etc.]", which could make a difference if a player plays with a borrowed deck. In the worst case, it could mean that all players play with cards actually owned by some other player in the same game... But even if someone does play with a deck borrowed from a friend, they still get to pick up that deck and go when conceding the game, and there's not much the game rules can do about that.)