Motorcylce accidents - is it an accident when you don't make a contact with a car?

I remember riding my GS650 down Fulton Street in the Western Addition of San Francisco one rainy evening a few years ago. I was going about 30 miles per hour when a car driver pulled out from the intersection without stopping to check for upcoming traffic and turned right into the lane I was traveling in. I tried my best to break and prevent the accident, my motorcycle skidded on a slippery road, while my body was thrown in the opposite direction. Neither I nor my motorcycle ever made contact with the driver at fault. 

When I contacted the other guy's insurance company, they tried to argue that because my vehicle never made contact with his vehicle, there was no accident and thus they should not accept liability for my injuries and damages. I had to admit that technically they were right. An accident is by definition is a collision between two vehicles or a vehicle and a body. However, I also believed that it was fundamentally unfair that a person who tries to avoid an imminent collision should be punished by not being able to recover compensation for his damages, while someone who doesn't care that much to avoid a collision would be compensated. I argued that even though there was no contact between the vehicles, I should still be compensated because ultimately I fell off the motorcycle due to the fault of that other guy. 

Eventually, the insurance company accepted my arguments and agreed with me, settling all my claims shortly after I finished my medical treatment.