Would you be more comfortable with "we can't estimate the probabilities of all failure modes"? I am sure that all engineers involved in planning the failure-handling systems know that those "calculations of probabilities" are only estimates based on some assumptions.
I think nuclear often gets bad press because you can measure and calculate a lot of risks to a much higher precision than in other industries. Like "x amount of radiation released" where x is actually a very small number but the fact that you can measure it and make an estimate as to how many cancer cases will be caused by it makes it scary, while people don't care much about the risks of, say, coal-mining because thats harder to measure/estimate.
Certainly they never go as far as voting against chicken farms.
Its got to be the theoretical nature of nuclear power generation that has something to do with it. Its invisible, unfathomable and secretive, so folks distrust it?
That's still too intellectual to make most folks even notice. California farmland is getting poisoned by selenium from groundwater wells, but not a lot of folks picketing about that.
In a disaster scenario the first reactions are generally passive (dropping of control rods, changing where water flows) and then "all" that remains is to cool the decay heat. Aye, here's the rub: the cooling system is not a passive system. It requires power to drive the water pumps for the cooling system that siphons the heat away from the reactor vessel. After initiating reactor shutdown the most critical time period is the first little while as that is when there is the most heat. Too much heat and it'll damage the fuel, vessel, and/or the cooling system and can effectively damage the reactor enough so to prevent it from ever recovering (thus, meltdown).
The questions left to ask are to what degree the cooling systems (primary and backup) are working, and whether they've been powered consistently. With that bit of information alone we'd be able to make a pretty accurate estimate as to the state of the reactors in question. What is scary is that it would be really simple to say that all of those systems are working as expected and that there is nothing to worry about. Since that hasn't been said I'm of the opinion that there is definitely something to worry about.