Accidents don't happen when cars are passing cyclists, though. Drivers notice this because they're inconvenienced, but it's actually pretty safe. Accidents happen at intersections, due to cars turning in front of bikes, or not being aware of bikes that are turning.
As for neck injuries... if a helmet increases my chance of a neck injury because it decreased my chance of a fractured skull, i'll take the trade.
That was my thought too when I read the claim about neck injuries. Does a helmet really increase the risk of neck injury, or does it just increase the likelihood of surviving the blow to the head that caused the neck injury? Wearing a helmet should have no way of affecting your neck unless you're being stuck in the head, in which case I would definitely prefer to be wearing one.
As for neck injuries... if a helmet increases my chance of a neck injury because it decreased my chance of a fractured skull, i'll take the trade.