When airliners (or any other high performance jet) run off the end of the runway, it's generally one of two things: landing long or spoilers didn't deploy. Hydroplaning or icy runway can be a cause of runway excursions, but far less than folks think and anyway, clearly not the case here.
Greenville is 7,000' long.
If you're used to flying a GA airplane (and it sounds like the pilots of this Falcon were primarily GA experienced) then that's several times the landing distance of a GA airplane. Super long runway. Or so you get used to thinking.
But for an airplane like this one, it's quite short. You have to get the airplane down, on the runway, weight on wheels/strut switch activated, so that the spoilers deploy and take the airplane's weight off the wings, only then do the brakes become effective. Reversers are an aid, but it's the brakes that stop the airplane. And they have to be in firm contact with the pavement.
You learn to fly on little airplanes, and then look at this "long" runway and think you've got room - but you don't. Very easy to make a critical mistake - float the landing (so the struts don't compress), land long, carry too much speed, or bounce the landing, and you're in deep trouble because effective braking doesn't begin until the landing gear are compressed and spoilers deploy.
I should add that a stabilized approach (on glideslope, on centerline, proper airspeed, proper sinkrate, proper configuration) helps with a good, on target, landing. It's a focus area for my industry, my company, and the FAA. Unstabilized approaches have been a factor in the preponderance of runway excursions - too fast, too high, etc. on approach, and you touchdown too long, especially if you're trying to "grease" it on...
From the speed with which the airplane left the runway - it either touched down way past the "touchdown zone*" or the spoilers weren't armed/deployed. It had far too much speed at the end. The gear were down, the optical illusion of the camera angle makes it look like the airplane is too close to the ground, but that's because the camera is looking up at a hilltop.
I used to land the 757 and the A-320 in Orange County/John Wayne all the time. 5,700' You HAD to be on the ground in the first thousand feet or you were at risk of not stopping. We did it all the time, but we knew exactly what we were up against. I used to fly out of LGA nearly every flight, in the 757 and A-320, only 7,000 with highways at one end and water at the other. Same deal: on the ground in the first 1,500' or we go around. Period. We had a rigorous touchdown zone defined and we put the airplane in that zone.
Never a problem stopping in either place, including when it was wet and/or snowy in LGA, because the airplane was landed properly, in the proper place on the runway. That made stopping uneventful. I am always happy when things are uneventful in my line of work.
* which we define as the first 1/3 of the runway or first 3,000 feet, whichever is shorter. But none of us would use 1,900 feet (the first 1/3) in SNA...that's too far down...