By the way, scratch the overheated brakes idea. Heading into Kings Canyon, at the point they went off the road, the last four miles before that point there was no descent.

Fresno Bee shows a driving video to the point in this article:
Car parts in Kings River

Using Google Maps street view, this matches the view at :26 seconds in the video:
https://www.google.com/maps/@36.8243676,...!7i13312!8i6656

It appears they were headed OUT of Kings Canyon (west bound). There is a hard left curve where they went off. The curve is preceded by almost a mile of nearly straight road. So maybe they were lulled into a false sense of security and safety.