He did all the singing and it will come close to fooling you until the credits when you hear the real thing.
But I was always wrong about so many things with Johnny Cash. When I was young, my Grandfather loved him. We would take weekly 2 hour trips to my Grandfather's camp and I had to listen to nothing but Johnny Cash for 4 hours/week.
So, I was wrong about why he wore black. I was wrong about when he wrote the song about Folsom Prison and pretty much everything else I ever thought I knew. My Grandfather had a way to tell a story
It is just worth watching to find out what you thought you knew about Johnny Cash was most likely wrong.