But then... why wouldn't he say that more precisely? If I had my documents encrypted with keys that I'd distributed to multiple parties, I'd be shouting it fro

But then... why wouldn't he say that more precisely? If I had my documents encrypted with keys that I'd distributed to multiple parties, I'd be shouting it from the rooftops: "No point torturing me, the key is in three pieces and if I don't sign in every week the data will be destroyed so realistically you can't possibly seize all the pieces in the time-frame you'd require! Of course, if you can get all the pieces, just stick us all together in the same room and I promise to give you my piece, so no point torturing me then either." Seems like there'd be a really strong incentive to have people know you had a mechanism that ensured it.