Auto Accident Fault?

I was stopped at a red traffic light in the right hand lane and I made a legal right turn into the near lane. I began to accelerate and I looked to my left rear and to my direct left to make sure it was clear and proceeded to change lanes so I now am in the second lane of a 3 lane roadway. When I turn my head forward, I see a man directly in front of me who had pulled out of a parking lot from the right and is attempting to cross the 3 lanes of traffic. I had to slam on my brakes, and as a result, I slid into his left, rear side panel. From my point of view, I clearly had the right of way and that other driver cut me off and is at fault for the accident. The man is uninsured and is now trying to make a claim for bodily injury and damage. I am dumbfounded as to why he thinks he has a claim. Any thoughts?