I thought the story went that the word "fighting" was added to the name after a violent street fight broke out between the students at the university and a group of KKK members who had come to South Bend.

Is there any truth to that?

Klan rally in late spring of 1924, basically leading to the elimination of the Klan as a viable political organization in Indiana. Prior to that, the Klan had grown to a major force in Indiana, basically controlling state politics. Within a few months of the riot, ND had won it's first consensus national football championship (4 horsemen year) and the Indiana Klan leader was convicted of 2nd degree murder. Go Fightin' Irish!