The point is that the nuclear fuel has now been cooled down. Because the chain reaction has been stopped a long time ago, there is only very little residual heat being produced now. The large amount of cooling water that has been used is sufficient to take up that heat. Because it is a lot of water, the core does not produce sufficient heat any more to produce any significant pressure. Also, boric acid has been added to the seawater. Boric acid is “liquid control rod”. Whatever decay is still going on, the Boron will capture the neutrons and further speed up the cooling down of the core.
The plant came close to a core meltdown. Here is the worst-case scenario that was avoided: If the seawater could not have been used for treatment, the operators would have continued to vent the water steam to avoid pressure buildup. The third containment would then have been completely sealed to allow the core meltdown to happen without releasing radioactive material. After the meltdown, there would have been a waiting period for the intermediate radioactive materials to decay inside the reactor, and all radioactive particles to settle on a surface inside the containment. The cooling system would have been restored eventually, and the molten core cooled to a manageable temperature. The containment would have been cleaned up on the inside. Then a messy job of removing the molten core from the containment would have begun, packing the (now solid again) fuel bit by bit into transportation containers to be shipped to processing plants. Depending on the damage, the block of the plant would then either be repaired or dismantled.
A Korean (nuclear engineer?) has been posting on somethingawful.com. Here's one of his posts. He also states that the reactors will be safe, mostly.
Without cooling water, the likely "worst case" will be the reactor pressure vessel (RPV) building up heat, which builds up pressure, which could cause a rupture of the vessel. The fuel rods will spill out radioactive contents, fires might break out, and the reactor is basically a lost cause.
And how does that affect the general populace in terms of radioactive dose?
-Not at all.
The Atlantic weighs in by comparing the Japanese nuclear crisis to Three Mile Island.