Black River Killer's first kill

I'm curious how all of you folks interpret the first verse of Black River Killer. Because the narrator never tells us whether or not he committed the first crime. So, do you think he did kill her and was always simply driven to murder? Or, do you think he was falsely accused, and the rest of the murders are for revenge?

Edit: I should probably give context for why I'm asking this. It's because, for a decade, I just assumed he had killed her. Then I took BRK to a voice lesson, and when I tried singing it as the character, I realized he probably didn't. Has anyone else really thought about this??? It's wild, because it changes the narrator's motivations for the entire story. Which is something I think about a lot as a singer. (I have no idea what Eric actually intended.)

I always thought the song was about an inability to adjust to normal life outside of prison, and that he didn’t kill the first girl. He then was driven to kill the second and third people by his time in prison. 

Great question for discussion. I agree, I don’t think he killed the first person, but was so destroyed by what happened after that he just lost it.