What could cause someone to remember things that happened to someone else, as if it happened to them?

I know someone very well. This person is close to me and we've been through the same life altering experience in our younger years. 15 years has passed and this person still harbors resentment and grief. They are quick to anger and highly emotional. Regardless, I've come to terms with the fact that I need to love them and accept them for who they are. There's just one weird thing that bothers me. There have been multiple times that I have mentally noted that this person will outright recall a memory telling a story, when that memory is actually MY memory. It's could be something I did, or said, or whatever, like I said it's happened more than a few times. I have a strong memory, I know for facts that these things the person speaks of are my own memories. I have brought it up and tried to correct the person, but they are insistent it happened to them which is extremely frustrating and just leads to conflict. How am I supposed to prove I lived my own life and that those are actually MY stories they're telling? This has got to be abnormal, and I can't find too much information about it. Thoughts?