It takes a pretty gentle team to be called "parade broke", perhaps these were not qualified. It's the owner's judgement call as to whether his horses are safe. My dad would never allow his team in a parade, even though they were broke to the highest standards. As a kid I was always mad that he wouldn't do it, but now after all of these years I understand.
Granted, accidents happen with even the safest of horses. We don't know that part of this story. Sad, sad deal.
HP