She probably picked up a nail or a had a small pinhole leak in the tire that went unnoticed, it could have even happened on the same drive that blew out the tire.
The black powder usually shows up in tires that are run on low air pressure. Basically as the pressure decreases the center tread of the tire starts to raise away from the road while the sidewall flexes more. When the pressure is low enough the sidewall starts to pinch under the rim or bends at too sharp an angle. When that happens the inside of the tire starts to disintegrate. If its not corrected, the inner sidewall keeps building heat and disintegrating and eventually the belts are no longer held in place by the rubber, which is what you are seeing, the separation of the belts on the sidewall.