If you read the interview, it's not actually about a girl cheating on him. It's about the way his mind worked when they broke up, the way he wanted something to blame for it going wrong and so made the assumption that she cheated on him; whereas in the interview it states that there was no cheating in the relationship.
Besides, it might not be literal. He could be referring to this girl 'sleeping in someone elses bed' after they split up.
I agree that this is amazing though. They played this song when I saw them on the 18th, it was beaaautiful! Brought a tear to my eye for sure.