I think the ideal action for motorists to take has become clouded in confusion over the years. “Lie in a ditch” is an almost unfathomable action. As you noted, panic derails rational thinking, and there is a human drive to seek shelter. Getting out of a car into insane wind, and likely heavy rain and hail, and possibly debris flying around, is the exact opposite reaction that is impossible even for me as a chaser to imagine doing. I’m not sure the average person understands that they should easily be able to drive away from a tornado as long as they are not crossing its path, and assuming of course they are not stuck in traffic. I seem to recall hearing that there has even been advice in recent years to stay in the vehicle, with at least some chance of protection from seat belts and air bags. I could be wrong about that, but even as a chaser the public safety messaging seems muddled to me, I can only imagine what the general public thinks.
I agree, there is no clear action or good choices presented to people.
However, it seems clear that the vast majority in these scenarios are not even really hiding from a tornado or imminent threat to their lives, but selfishly worried about hail damage. If they were worried about their lives, way more people would flee when a threat is clearly in one direction. Most overpass blockages happen well before the storm is right over the overpass. Meanwhile I often see truckers keep trucking into black clouds or right toward a tornado crossing an interstate because their mind is on money and unfair schedules. These types of emotional reactions are part of human nature, but generally many of us lack situational awareness or have pre-planned for what-if scenarios.
There is almost no safe message that can be taught to the public without more context such as teaching them to accurately read radar (and make sure it is up to date). If they are told don't drive, they will shelter somewhere stupid. If they are told drive away, you will see an increase in panicked flight such as happened 5/31/13.
Some of the people who freak out and just freeze with plenty of time for other choices are much like deer in headlights. Their brains shut down. Not everyone has the mindset or training to handle high stress scenarios without such mistakes.
As frustrated and even outraged as I am about these types dong things that put many others at risk, the best we can all do is try to plan around the natural tendency for enough people to behave like animals in any impending emergency to cause problems in their wake.
In a strong tornado, I think a low lying ditch may actually be a better option that a top heavy vehicle wind can get under (for example look at cars crumpled after well known fatality events). From a ditch, there are a lot of soft spots to land if you are not picked up and dropped from hundreds of feet up, and the chance of avoiding a car crushing in on you is great. Debris would also likely flow tangent over the ditch if not too shallow. No options are good if stuck in a tornado, but unless the public can be taught what is a strong tornado, how to use a basic tool like radar, and when to evade, they will continue to panic.
It would be nice if warnings could work like aviation TCAS where aircraft are warned they are imminently in the path of another and each pilot gets immediate instructions to go a certain direction (up, down, left, right, or a combo) to increase separation to try to avoid a crash. This could maybe be done in real time sometime soon with storm tracks, instead of just a yelled alert on your phone that "you are in a tornado warning! - panic immediately"