It's possible to design a reactor in such a way that it is impossible for it to melt down. The maximum temperature achievable by an uncontrolled reaction, according to the laws of nuclear physics, is less than the melting point of the fuel itself.
True. I believe they're called "pebble reactors". The fuel looks like golf balls (maybe larger) rather than fuel/control rods. I don't know the physics behind it, but the reaction is self-regulating such that a "China Syndrome" is highly unlikely if not impossible (famous last words, eh?!). Anyway, it's a much safer reactor than the current design.