Some myths considered:
Custer was beginning to bald and had a butch cut for the campaign. He didn't have long flowing hair.
It is doubtful that Custer carried a sabre into the battle. So ignore the paintings showing him with one.
The proffered gatling guns were being transported by condemned mules and would have slowed down the column considerably.
The Lakota didn't know who Custer was. They did celebrate the death of their arch enemy Mitch Boyer who was a scout for Custer. The Cheyenne recognized Custer though.
No band played during the battle.
Oops.