Yup, this is the primary case where the rear vehicle isn't at fault. You change lanes into a lane that's moving faster and get hit, you were wrong even if they hit you from behind.
If it can be proven. 25 years ago a scam was where someone would suddenly change lanes to be rear ended like that, then claim "back pain" and sue for a lot of $$$. I don't know how common it was, but when there are not witnesses the courts tend to side with the person being rear ended.