What Flipper is saying, and I watched the WT video also, was:
1. Destroy any 'extra evidence'... like notes, phone records, letters, anything that can be used in court as evidence to support what happened.
2. They are not telling them "destroy the fact that they were DFd" (although I would say that they try to hide WHAT they were DF'd for, by saying something like: "Oh, he stole something from a store (which they DID do), or they were smoking (which they did) or "they got drunk" (which they did) and then not mention that the person also molested a child.... After all, they are now 'disfellowshipped.'
Like Flipper said, they do not trust the rank and file, or 'elders' to keep things secret. What if a wife found a notebook in her home, and read the notes about an abuser? WT does not want elders to keep any personal notes or evidence.
WT does have a good knack for 'hinting' at what they realllly want people to do without realllly saying it. I am sure some elders will take the 'destroy all evidence' to the next level.