I would strongly guess that two factors were at play with the crash:
Maintenance....because what I am reading sounds an awful lot like a "split flap" condition causing the abrupt roll and stall/crash. While very rare, it is a known condition that can occur on the Caravan. In the US, it is a 100 hour inspection item, as I remember it. What takes place it a pilot selects take off position on flaps, maybe 20 degrees on the Caravan, for a short field, high altitude take off, and as soon as a positive climb is established and obstacles (like trees, towers, mountains) are clear, flaps are retracted to "clean up" the drag...flaps create more lift at the cost of speed and drag, and short field take-offs need more lift. I would say from the witness accounts that the airplane "suddenly" veered left and rolled, which says in all likelihood, that one flap retracted and the other remained down, which acted like an aileron, lifting the wing, and rolling the aircraft...close to the ground, by the time the pilots knew something was wrong, they were already in the fireball.
And, pilot experience. If it was a split flap, you have to have your crap wired tight and be quick....a few seconds kills. The minimum time as pilot in command of a charter like that in America is 1250 hours. Typically the first officer also. I notice they referred to "both" pilots as dead, but outside the US, it is very, very common to see single pilots on charters with 30 or more passengers.
The proper way to handle short field take-offs like this would have been for one pilot to fly, and the second to manage power and flaps. If I am right, and it was a flap issue, the second would have put full flaps down and power to 100%+ while the pilot used his strength to force the airplane wings level. These are not "boosted" or power controls, so it takes physical strength to hold the plane level in such a scenario, and if the pilot felt the plane roll, his instinct would have been to roll the control wheel opposite of the roll, and that would have increased drag and the resulting stall/crash. All of this would rely on the instant analysis while the flaps were retracting...maybe 3 seconds, that something was wrong, and then doing everything right. There is no do over outside of a simulator.
In the US, pilots get the advantage of simulator training complete with every known accident/incident/event that can happen....and they train for it. Like the plane that landed in the Hudson, all airline pilots now train for dual engine or complete engine failures, as opposed to when I was doing twin engine training, we trained for one engine failing. Not both.
As mush as I hate regulations, I am both an experienced pilot (3900+ hours), and a licensed air frame and power plant mechanic, and I WILL NOT fly outside the US unless I AM IN THE PILOT's SEAT! We take our safety for granted, and it is due to our heavy regulations, but in the case for safety, it pays.