You can dramatically slow reactors down, but you can't actually 'shut down' because simply decay produces significant amounts of heat. So the real problem at Fukushima was the need to be able to passively cool a reactor indefinitely in that 'slow' state without human interaction and that's where they failed. Sure, if they had power and none of the connectors had failed it would have also been ok, but without long term passive safety nuclear power is not safe.