Ok, there is a pretty decent history between Jimmy Kimmel and Matt Damon. At the end of his shows, it became a joke for Kimmel to bump Damon even though he was never scheduled to be a guest. Then Damon was brought on to the show as a guest and was bumped right away.
Guillermo, Kimmel's sidekick went to the Oceans 13 premiere to "interview" Damon. Again, Damon was bumped due to time restrictions:
When the Bourne Ultimatum came out, they did a reinactment where Guillermo bumped Damon from his role as Jason Bourne:
So there's your backstory. I suppose the "I'm f'in Matt Damon" video was Damon's hilarious form of payback. It was going to be on Jimmy Kimmel Live for Kimmel's 40th birthday but that show didn't happen due to the writer's strike.