In the story, it was heavily implied that Fred Collins was in a Union (Northern) regiment, but in the video he was a Confederate soldier. Why would...

I know the video that you are talking about.  It was made in 1977, and it was done in black and white.  It is possible that the filmmaker chose to make Fred Collins a Confederate soldier, because the audience wouldn't be able to tell that Collins was wearing blue.  A blue uniform in a black and white film would either look dark gray or black.  An audience would assume that a soldier in a gray uniform would be a Confederate soldier. It might have just been easier to change the army Collins was fighting for rather than trying to get the audience to understand that his uniform was blue. 

Another possibility might be because choosing the Confederate army fit better with a theme of the story.  Collins's efforts were wasted, because other soldiers knocked over the bucket.  Essentially, his efforts were futile.  The Confederate army ultimately lost the Civil War, so perhaps their efforts can be seen as futile too.  Making Collins a Confederate soldier reinforces that concept of Southern futility.