Much of that was due to the international investigation team not being able to get there due to it being an active war zone. In fact the Ukraine made it worse by starting a campaign to take back the nearby towns, which is actually hampering the investigation now.
While there probably was some looting much of the complaint was the rebels were moving items around, especially large ones. That could be entirely consistent with searching the wreckage for bodies. It appears they were far more methodical than we first though, going as far as numbering the body bags (assuming there are corresponding numbers on the ground) and storing them in a refrigerated train carriage bear the site. That has now been moved into non rebel areas after agreement was reached and after being held up near Donetsk due to the Ukrainian offensive in the city.
The black boxes were collected and stored, before being handed over last night. Seems reasonable...
It's a war zone, as mentioned previously think of the uproar if one of them was shot! Initial refusal for them tsearch the cash site could have been down to the leader at the site not being told by superiors, or just being obstinate. They aren't a fully organised force, as seen by the drunkenness, although that could be put down to the horrors they mush be seeing at the site (equally it could be due to guilt at shooting it down in the first place).
While it's great to jump on the suspicious wagon there are also plenty of reasonable explanations that can be gleaned from the information we are provided, especially when we ignore the obvious political posturing by the west and Russia. The problems could equally be in part caused by the rebels exerting their control over the area as a political move... Obviously there could be some pressuring from Moscow with all this as welll.