keeping that following distance at 5 or 6 might have helped slow down sooner, giving her a chance to react like the car in front of her did. The data never lies, follow the facts. We don't know, but Tesla does know how her car was configured, and if she was following too close at too high a rate of speed and not being fully aware of her surroundings or upcoming traffic (e.g. other cars traffic lights signalling a slowdown or obstruction in the road), then yes it may have been her fault, not the auto-pilots. It only does what it is told (and programmed to be capable of doing).
Her case is described in the manual very clearly:
"Warning: Traffic-Aware Cruise Control can not detect all objects and may not brake/decelerate for stationary vehicles, especially in situations when you are driving over 50 mph (80 km/h) and a vehicle you are following moves out of your driving path and a stationary vehicle or object, bicycle, or pedestrian is in front of you instead. Always pay attention to the road ahead and stay prepared to take
immediate corrective action. Depending on Traffic-Aware Cruise Control to avoid a collision can result in serious injury or death. In addition, Traffic-Aware Cruise Control may react to vehicles or objects that either do not exist or are not in the lane of travel, causing Model S to slow down unnecessarily or inappropriately."
The problem is who would want to read the manual?