What rim size and what tire width? This sounds like a problem I had with my Speed Pro TT when I first got it. The previous owner had mounted 2" Big Apples that barely fit the inside the brakes. I initially thought the wheels were out of true until I swapped the stock tires back on and realized how narrow the rims were. The BA's were just way too wide for the narrow rims.
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C'dale BBU('05 and '09)/Super Six/Hooligan8and 3,Kona Dew Deluxe,Novara Buzz/Safari,Surly Big Dummy,Marin Pt Reyes,Giant Defy 1,Schwinn DBX SuperSport,Brompton S6L/S2E-X/M6L-X/S12 T Line