It's very relevant. Suppose the cake has 3 butter roses, and Charlie LOVES them. He cuts the cake into 3 pieces each with a rose on it, to get one in any case.
Alice picks one piece, Bob picks another, Charlie gets the third.
Now Bob thinks his piece is a bit too small compared to Alice's and transfers Alice's butter rose onto his piece.
Alice either swaps or doesn't.
Charlie now sees that either Alice or Bob has a cake piece with TWO butter roses and is VERY envious.
He sees alice or bob with two butter roses on top of a smaller piece.
Charlie has the first cut, so he can cut horizontally and make a tiny piece with 3 butter roses on top. he either gets his three butter roses or a bigger piece of cake, their relative value is still the same for him.
Alice picks one piece, Bob picks another, Charlie gets the third.
Now Bob thinks his piece is a bit too small compared to Alice's and transfers Alice's butter rose onto his piece.
Alice either swaps or doesn't.
Charlie now sees that either Alice or Bob has a cake piece with TWO butter roses and is VERY envious.