Not to mention the backup generators were taken out by the flood, not the earthquake or epic winds. I highly doubt a tornado would cause damage (at least where it matters) to a Nuclear reactor. There is a slight chance a Hurricane could send in a surge that could affect a nuclear plant by the ocean, but even then the strongest hurricanes don't send a surge anything remotely close to the Tsunami that ripped through Japan. And remember this is a part of the world that gets some of the most intense storms out there. I am pretty sure the plants were built to withstand them. Hell, I am sure a few have blown over them, though I can't say with certainty.
We have more nuclear power in northern IL than in any other part of the US. We also get a lot of tornadoes here. Many have passed near the nuke plants, but breaches were never a concern - the winds are not going to crack the thick concrete of the reactor. It's much stronger than any tornado shelter I've been in. There could be a lot of damage to the connecting grid outside, but the backup systems are safely within the building and an orderly shutdown would proceed until exterior repairs could be made.
As noted, it was the powerful tsunami right after an historic quake that combined to cripple Fukashima.