ICAO Annex 13 tells us that the State of Occurrence has primary jurisdiction of accident investigation, second would be State of Registry and final is State of Design. I think one reason behind this chaos might be is up until now nobody knows who has jurisdiction of the accident because the wreckage hasn't been found yet.
There is an ongoing territorial dispute among Asian and Chinese right now about who owns the south china sea so this might also complicate the matter... just my two cents
