Must an "accident" evolve from human error?
Solution 1:
Fundamentally, you are right. "Accident" does not need a human agency, or even an animate one if we're going to be really picky. Accidents happen; that's rather the point.
The only justification for not using the word "accident" in conjunction with the events at Fukushima is if you believe a design flaw or similar was responsible for what happened. Since that doesn't appear to be the case, stand your ground and reclaim the word!
Solution 2:
Accidents arise from chance, but I think there is also some element of human error necessarily involved in an accident. For example, you may have been in a car accident because of chance (a deer running across the road) and human error (not being attentive enough, failing to stop in time).
This also applies in the case of the Japanese nuclear incident/accident/situation. The situation was primarily caused by chance (a tsunami), but also by human error (failing to plan for flooding of the building and general power outage).
Solution 3:
There was just a news story that hospital emergency rooms in the UK were no longer allowed to put "accident" on a report - everything must have a cause, and presumably somebody at fault - implying that an accident is an event with no human cause.
Ironically since the ER in the UK is most commonly called accident and emergency.
Solution 4:
Depending on who is doing the censuring, it is typically best to play ball and find another word. That being said, I find no problems with using the word "accident" to describe events as the word is defined in a dictionary.
It does feel a little strange to suggest that a tree falling on your house was an "accident" but I find it feels odd more from disuse than misuse:
The tree fall on my house! What a terrible accident!
It seems more suitable to use "accident" this way when the victim was human:
I had an accident with a tree. It fell on me.
Causation isn't necessarily implied (I didn't knock the tree over) but it feels less strange in my mouth.
Accidents can also be attributed to non-human wills or causes (even if they are really just autonomous entities):
The dog had an accident on the rug.
The computer accidentally crashed.
And the ties are loosened further when talking about accidentally doing something:
The planet accidentally destroyed its own moon.
Part of the advantage of using accident is that it softens the blame of a tragedy or event by shifting the causes onto uncontrollable chance. A more direct attribution of fault would use words such as mistake, error or problem. Ignoring the blame as much as possible could be accomplished with words like tragedy, horror or event.