From 3:24 to 3:27 it shows them taking something I can't identify (but not body parts) to a large van and the audio has the correspondent explaining they've been watching plane parts being driven away. But you're correct that video doesn't show the vehicle actually in motion.
The emergency workers themselves said in a few interviews that they too had to comply with the rebels demands pointing out that the rebels had all the guns and they had none. I believe I read the emergency workers were out of a local donetsk office in rebel held territory but part of the Ukraine government. If that's true seems like they'd have fled or been dead long ago. Lots of strange relationships.