Very sad to hear this news today. RIP folks.
With a relatively clean slate in terms of non-human error hull losses, Gulfstream seem to have been putting out a statistically very safe line of aircraft.
One has to wonder if the addition of Fly By Wire into the 650, might not hold a clue to what went wrong here. In general the entire range is pretty docile throughout the flight entire flight regime - this sounds like something to do with controlability, or uncommanded flight control input. In my mind, the company has pretty much just improved on its existing line and design philosophy with each new type - this is the first model that has strayed from Gulfstream's mainstay of mechanical controls and direct pilot input. Airbus also struggled in the beginning with the A320. Hope this is not the case with the 650.