While scanning the comments on Slashdot regarding the article linked yesterday, I found this description of one of the new "safe" reactors:
The pebble bed reactor (PBR) or pebble bed modular reactor (PBMR) is an advanced nuclear reactor design. This technology claims a dramatically higher level of safety and efficiency. Instead of water, it uses pyrolytic graphite as the neutron moderator, and an inert or semi-inert gas such as helium, nitrogen or carbon dioxide as the coolant, at very high temperature, to drive a turbine directly. This eliminates the complex steam management system from the design and increases the transfer efficiency (ratio of electrical output to thermal output) to about 50%. Also, the gases do not dissolve contaminants or absorb neutrons as water does, so the core has less in the way of radioactive fluids and is more economical than a light water reactor.
There's another design, whose name I can't remember, that uses a liquid metal of some sort as a coolant (lithium?) This oxidizes slowly on exposure to air, creating a kind of self-sealant which ensures no leaks in the event of a containment breach.
While certainly not fool-proof, both designs (and the PBR in particular) seem to be far safer than any existing reactor design currently operating. Considering these older, "less safe" reactors have experienced exactly one accident in fifty years, an accident that it must be pointed out was contained and handled as designed, it would seem self-evident that these new designs are quite safe indeed.