I think you got the wrong idea about what I said. Especially as I had already mentioned the situation being chaotic.
But let's just say, for arguments sake, that they just smother the site in concrete. Now they've got fuel elements encased either directly within concrete or more likely in unmanagable voids, either way, heat builds up. Whether that's enough heat to melt the materials (or melt them further), or not, you should still consider the old adage of P1V1/T1 = P2V2/T2. If they've completely sealed the thing with any significant amount of gas, pressure builds up, catastrophic failure occurs. If they've not completely sealed it up then escaping gas (itself radioactive or otherwise, I'm not too sure how much radon/etc there'd be from the given mix of fuel products, but it'd be there) is going to bubble radioactive liquids/particles in liquid suspension through the cracks.
Whatever happens, there's no way of getting in there and making any necessary adjustments to the system.
Encasing would require decent 'inspection hatches'-cum-venting systems and monitors at a bare minimum. You couldn't even just get away with embedding monitor of various kinds (temperature, pressure, geiger, etc) and small-bore tubes for dumping extra moderating liquid in and controlled extraction of gasses, because the monitors could fail and tubes could block, so you need to be able to retrieve and replace the instruments and deal with structural deformations in the exhaust systems.
Chernobyl might be considered "overly open" (birds fly in and out of the central area, apparently... not sure how many times they'd be able to do that, though, I'm out of date on the internal conditions at that site) but it at least provides passive air-cooling.
Personally, I'd go for two things: emergency water-retaining structures (caps on potentially overflowing drains, and otherwise put a rim around the site) and then try to arrange to more or less permanently re-roof the reactors themselves to prevent indiscriminate rain entry, although with an integrated controlled water (and/or boric acid or whatever) delivery system for use when needed and infrastructure for delivering remotely controlled mechanical equipment to undertake a proper decommissioning. But there are problems with that solution.
And not just related to the most basic difficulties of construction and the obvious flaw with the whole "roof the site off" plan. Given that the place is still in a quake/tsunami zone you have to account for the distinct possibility for more shakey-shakey and wavey-wavey for... well, the centuries you'd have to expect the site to have to be maintained even after the last of the more troublesome fuel is removed. Dounreay, sitting in a fairly geologically stable location (although as susceptible to tsunamis from random underwater sediment-slopes shifting as just about any other place facing out to sea, even without a handy quake zone) in a (IIRC) hard-rock area has been worried about this problematic disposal shaft of theirs (that I mentioned) being subject to coastal erosion over the coming 400 years...
And I personally think that there'll be no more than a "warm spot" of radiation-related illnesses. There'll be over-exuberant banning of fishing and farming in the affected areas, the zone will be left unpopulated within at least the immediate vicinity (not to wish to sound so casual about any aspect, but there's a whole lot more population upheaval gone on due to the original quake/tsunami incident[1], so any locals permanently evacuated from the vicinity will be very much a drop in the ocean in the grand scheme of things. On the border between statistically significant and not so... It won't be such a complete an evacuation as the USSR could so easily achieve (mostly due to relative population densities and the different degree and nature of the authoritarian governments involved) but it won't be 3rd-world-like in that there'll be significant underclasses (or oppressed locals or dispossessed immigrants) who find themselves unwittingly/unwillingly/unconcernedly living next to a disaster zone like you might in cases such as Bhopal or down-river of toxic gold-digging operations and their unstable dams in the Amazon.
I also think that they will get over it psychologically and socially, although I must admit that my previous opinions that there wouldn't be mass protests about the nuclear power have already been overturned, so I'm perhaps now less inclined to go with the whole "they are a stoic people" assumption than I was. Still, I maintain it'll never get anywhere near Libya-level protests, probably not even close to those we had over here, last weekend, regarding these stupidly regressive budget cuts being foisted upon us. And I know I'm setting myself up for another fall by being so bold in saying so.
On the whole, though, regardless of what opinions I might have asserted above, I'm also one with Niels Bohr, when he famously said "Prediction is very difficult. Especially about the future. Time will tell, and there will be more facts that I don't know about this situation than ones I'm definite about (and I'd bet I'm even wrong about some of the latter).
[1] There'll be a mix of those (who survived) wanting to move back to "their land", much as everyone did after the Great Fire Of London, down to demanding that they have their exact same plots of land, and those who would never live on the 'coastal plains' again. Together with the losses of life in some areas having significantly depopulated areas, it's entirely possible that the