It seems everyone here has forgotten about power steering. I see numerous references to "Steering Lock", however that's a totally different system. In most cars, when the car is off, the steering column itself will lock to prevent any turning of the wheel at all. This is a theft deterrent feature. Sometimes when the car is off you might be able to turn it left/right once or twice before it locks.
THEN you have Power Steering, which is either hydraulic or electric. Either way, the car needs to be on for it to function. Hydraulic required a pump to be active, and electric is pure electrical motor assist. Hydraulic systems will still operate for a few turns once the car is turned off until pressure is lost due to lack of the pump running, electric power steering will cut out as soon as power is lost. The reason why you wouldn't want to just *TURN OFF* the car at 125mph would be you would lose power steering and lose total control of the vehicle. Let alone you would also most likely lose power brakes, and make it *MUCH* harder to stop. Essentially turning your car into a speeding bullet in which you have little to no ability to turn or brake. This is why it's Neutral only or bust, so you won't end up flipping your car.
This same thing happened to me about 8-9 years ago .I was actually bringing my elderly grandmother back from visiting a relative, coming down a hill with a 7% grade that's a slow left hand turn for over half mile to 3/4 mile. It was my parents car, automatic. To save on the brakes I normally would downshift from "Drive" to "3" (It was a 4 speed auto and had gear selection of 3, 2, 1, or D). This is normal practice for cars. However in the shift, the onboard computer had a brain fart and the car shut off. I had no power brakes, no power steering, going down a 7% grade left hand turn. The only way to restart the car would be to pop it into Neutral and restart. The shifter was on the column, and at the time I had to use both hands with excessive force to keep the wheel turned to prevent smashing into the side of the road, not a option. I kept as calm as possible and managed to get to the bottom of the hill and managed to slam the brakes hard enough (pressing down as hard as i could for 30-40 seconds) to slow down enough to pull over and stop the car.
Come to find out the car had shut off on my parents like that once before, and once after this incident. A little after the 3rd time we got notice of a recall to reflash the onboard computer because of the very specifc problem where certain conditions it would cause the car to shut off. After the reflash, it did it one more time, and a few months later there was another recall stating the first recall didn't completely solve the problem. Fortunately we had already ditched the car. (2001 Mazda Tribute, same as Ford Escape if anyone is wondering).
So the man flying into the ditch my bet is the car running out of gas. As it sputtered, full power remained so he had access to power steering and brakes, and was able to slow down *SOME* from 125mph. When the cars engine finally shut off somewhere between 0mph-125mph he lost power brakes and steering, and was unable to control the car and ended up going off the road into a ditch, fortunately at a slow enough speed where he didn't sustain as much damage as he would have had it been 125mph.