To Floyd Landis, one of the mysteries of his time with the U.S. Postal Service cycling team was why more new bikes weren't available for the riders. He eventually struck on one possible answer: the team was selling equipment to the public to raise cash.

In March 2004, during an eight-day race from Paris to Nice, Mr. Landis said he was in position to win the sixth stage when his bike frame snapped. He blamed the mishap on the bike's carbon frame, which, he said, had been weakened by wear and tear.

After...