Smart move
The locals (civilian and otherwise) made all the right moves here (the initial shot aside, if it was them). They quietly found and picked up the bodies, collected most possessions, found the black boxes...
AND GAVE THEM TO THE RIGHT PEOPLE -- the recorders to the airline which owned them, the bodies to the country which lost the most. Not to middlemen (Russia, Kiev, whatever supposedly neutral international investigators were coming). What does USA have to do with this? did they even have a single soul on board?
They also videoed most of what they're doing, so if people would just stop editing them , they'd tell the truth of what went on. They did the work while everyone else is still just screaming invective at each other.
The Mayalsians, if they have any sense, will ask for blackbox help from Australia, who they already have arrangements with because of MH370, and not let the US get their hands on them either.