My take on how this works, in summary:
he distributed something totally unrelated to some people, quite a few of them, not even friends probably, with the instructions to do some non-specified action with that thing if something bad happens to him.
Those non-specified actions on those non-specified things, once done together by a minimum number of different actors, act as the famous dead man switch, which is therefore impossible to intercept via MITM attacks and impossible to beat,even by torture, because every actor could only know his/her specific action.
For what we know he could even have "outsourced" the whole setup to someone who then fleed/changed identity, this way not even him may be able to tell what actually has to happen in order to trigger the release of the documents.
Actually multiple persons in my idea were added just for the sake of redundancy, namely to avoid that the disappearance of someone involved would stop the process as a whole. The system in my opinion will then always work if the minimum number of actors is present.
You pretty much nailed how it's done, good show for off the cuff. Encrypt file with large symmetric key. Slice into n pieces, where n is like 5-10 or more. Distribute a few copies of each slice to reliable people unlikely to directly conspire. Distribute encrypted file widely. Give instructions on how to gather as a group based on some basic trigger. The chance of the gathered group missing every copy of one of the slices is pretty low as long as nobody gets a master list of key holders.
[edited for clarity]