Is it possible to forgive adultery simply because he/she is “never gonna dance again”?

The chorus of the song ‘Careless Whisper’ goes:

“Should’ve known better than to cheat a friend
And waste the chance that I’ve been given
So I’m never gonna dance again
The way I danced with you.”

Which leaves me wondering, do you think it would be possible to forgive a romantic betrayal, if the person said something like this? Would it depend on what the betrayal was, and/or how they expressed their regret, or what they said about the future?

(question improved by @Zaku)