Does a driver have a right of way in both lanes of a four lane street?

Question Details: I was attempting to turn left into a 4 lane street from a parking lot driveway. The driver on my left in the lane closest to me signaled to turn right into the driveway where I was exiting from. The next lane over was clear. So as I slowly moved forward into the lane closest to me then looking if it was clear of traffic in the opposite direction we crashed in the next lane over. I hit the center of his vehicle on his passenger side as he was trying to avoid me. He apologized to me and said he changed his mind. He didnt turn right as he signaled but changed over to the next lane and tried to go straight ahead instead. He told two police officers there that it was his fault. His insurance company says now Im the one who is at fault(I couldnt believe it!) because he has the right of way. It didnt matter if he signaled to turn right or changed his mind. Does he still have the right of way if we crashed in lane that he was not originally driving in? Doesnt he only have the right of way in the lane he was drving in and not in the lane over too? How can a driver have the right of way in both lanes and not be responsible for the controls on his vehicle or drving in a careless manner?

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