I want to say this right now. 4Kids owned the Japanese BGM for One Piece. Not sure if they bought it seperetely or picked it up along side the license, but they most certainly had it. Otherwise, they wouldn't have dubbed We Are, Memories, and those uncut episode (the later two never showing the light of day, outside Memories on the Mexico broadcast).
Most shows 4Kids have licensed in the past were from TV-Tokyo, in which their BGM rights would come with the Show. This is because TV-Tokyo typically funds and handels production of the music for the show when it broadcasts on their network. Only recent exception I could give is like PPGZ, which Aniplex handeled the BGM production/funding.