Fail safe or Fail unsafe?

The blowout preventer that failed in the BP oil rig disaster was meant to be fail safe. But why did it fail? There is an excellent video from the NY Times explaining what could have gone wrong. Layers of protection analysis is supposed to find these weak links, but in my experience, LOPA depends heavily on the time available for the team to do it, the experience of the team and finally what is done with the recommendations. Watch the NY times video in this link.