Also not a physicist, but...
After the accident, I did a LOT of surfing in an attempt to find out what was going on and what might happen.
It appears that, although any nuclear accident is not something to be taken lightly, this type of reactor can never truly have a "meltdown". A meltdown is where the fuel actually melts and cooks its way through the containment vessel. Even the Chernobyl "meltdown" only made it to the sub-floors of the building before stopping the burn. The reason why that happened was because there was not containment at Chernobyl. The melt left a melted pile of nuclear material called "the elephant's foot". Google it, there's pics... The radiation from that pile was so sever that it killed several robots before they were able to get one close enough to take a picture. Somewhere around 15 or 20K rads if I remember correctly.
I don't understand the precise details, but from what I read the light water in these reactors is actually part of the medium that controls the reaction. As water levels drop in the core, the sleeves (made of zirconium oxide) holding the fuel can heat up and melt, exposing the fuel, which could possibly drop to the floor of the vessel. But the material itself, a ceramic form of uranium, which from what I have read, is incapable of the heat levels of the Chernobyl reaction. Also, with the water level drop, they supposedly cool down on their own after a few weeks...
But when you factor in an earthquake, tsunami and fire, things probably get a bit more complicated. In all likelihood, at least some of the fuel has dropped to the bottom of the containment vessel. They really won't know for some time, as there are so many variables that have to be considered and eliminated before they can even go in to take a look.
Further, if these reactors should somehow find a way to "meltdown", their design is such that the fuel would burn through containment into a specially designed cavity under the reactor vessel that disperses the fuel to the point where the reactivity would diminish to the point of making it a "cleanup job".
Luckily for everyone, they don't appear to be heading that way...
But again, I am not a physicist and there's always the chance that I have misunderstood or misinterpreted something, so there's my two cents...If there are any physicists out there, love to hear from a pro.