I'm pretty sure that that is backwards: the generators absolutely had to be running, as there was no electricity and they were the only way to get power to run the pumps to cool the fuel.

I am conflicted in nuclear power. The present system for both Japan and USA to store high-level nuclear waste on site does not seem to be a good one. Obama shut down work on Yucca Mountain repository and I think that was a political, not science, decision.
Chris