There's another rivalry involving Brazil's Team.
Brazil vs. China
This one was more like a backstage rivalry and started in 2002, when the Chinese Team lost on purpose both for Greece and Korea to avoid meeting Russia in the semifinals.
Despite the middle-finger episode that was mentioned here, which didn't happen as far as I'm concerned. Many others happen, like the meeting of all the teams in the cafeteria of the hotel they were before the quaterfinals, when the Chinese Team appeared and the Brazilian players started to applaud them with irony and then all the other players from other NT's started to applaud them too.
After that, in the press-conference after the quarterfinals match which Brazil was defeated in the tie-breaker, both the coach and the captain of Brazil's team deliberately said they almost screwed China's plan and that they were sure China would lose the semifinal match.