The T/Rs are held in the open position solely by continuous application of hydraulic pressure from the onside hydraulic system through the T/R control valves mounted in the aft equipment bay. (The "boiler room" in Gulfstream parlance) -
The combined hydraulic system supplies pressure for left T/R, and the flight system supplies the right T/R.
As I mentioned in a previous post, if the T/R's are opened during maintenance by the use of an external hydraulic cart ("mule"), and the pressure from the cart is then reduced to zero, the T/R buckets can be pushed closed by hand with a bit of effort.
The combined system supplies the landing gear actuators, so the pressure and return sides would have been breached the moment the nose gear was torn off, and even more so when the mains departed.
Both flight and combined hydraulic systems would have been further breached by the contact of the wings with the localizer antenna, as both systems supply the aileron, flight and ground spoiler actuators through multiple lines on the rear beam of both wings.
Once the airframe started coming apart, I would think that any if the normal electrical and mechanical T/R control systems would have been rendered inoperative in any case, but with the loss of hydraulics, inertia could easily have slammed the T/Rs closed, as the aircraft slid though the terrain off the end of the runway and decelerated.
Not "proven fact", but it seems the most likely explanation to me.