I'm not arguing against insuring negligence, I'm arguing against calling negligence an accident. It's a neat way of removing culpability. "It was just an accident!"
"An accident is an accident" was being said by the insurance specialist, and in reference to the insurer's responsibility. In context, it was meant to say nearly the opposite of what you're inferring - something more along the lines of, "We can't pick and choose like that." Which is true; doing so would defeat the whole point of mandatory liability insurance.