You need to realize that all cars are looking for ways to kill you and get away with it. They'll try stuff like your accident when ever they have a good enough excuse. It's pure malice on their part, and it only comes out looking like an "accident" because they wait until it will look like an accident before they try to kill you. "Obeying the rules of the road" works great when the police show up, and it works fine in court, but you need to realize that wont matter a lick if you're dead or unable to walk.

It's not exactly as bad as I paint it, but following this belief is a whole lot safer than relying on drivers to respect your rights. In approaching an intersection, you should never allow a car that MIGHT turn right to have the chance to cut you off like you describe. Enter the lane behind the car rather than stay in the bike lane. At every intersection, you should never never never be in the bike lane.