The only way I would fight this is if you were on-time ready to work, got all your things together, and simply forgot to punch in. Actually arriving late though do not bother. And the best way to fight being sent home (in general) is to raise your voice and raise hell until the steward hears you.
Here we regularly have late punches because the clock-in machine might not have been set up correctly or there was simply a line in front of it at the start of the shift.
Supervisors working is something separate, I would talk to your shop steward. Where I am, someone else would volunteer to file to earn some bennies and keep your name out.