In my perception, it shows that nuclear plants are able to sustain damage during such a massive earthquake without causing significant harm to their surrounding, all while the oil refineries are burning…
The World Nuclear Association has said it understands the situation at the Fukushima Daiichi nuclear plant is "under control", and that water is now being pumped into its cooling system. The Japanese government earlier declared an emergency as a precaution and evacuated people living nearby, after there was a malfunction and the water level began to fall. A WNA analyst said the back-up battery power system was now online.
If the power going out is enough to potentially cause a nuclear meltdown, I'm pretty sure that's indicative of flawed technology rather than some problem with public perception.
Most nuclear reactors will automatically scram if they lose power. The control rods are held up with electromagnets so they will drop if power is lost. Losing power isn't too dangerous. Loss of coolant is quite dangerous but there are backup systems that can flood the reactor with an alternative coolant source. For example a submarines can flood their reactors with seawater. You just don't want to do that except in an extreme emergency because it will destroy the reactor equipment.
Edit: It looks like the reactor had a coolant pump failure. The loops are intact. There is time to do something about this. The water has to boil off before anything really bad starts happening. At this point they would be concerned with saving the reactor from damage. Declaring a nuclear emergency is still a good idea. This is dangerous but not anywhere near three mile island. They know what's happening inside the reactor and can handle things accordingly.