I'm confused. Are you saying that although you canceled your contract three days before the termination date, you didn't cancel early? Three days before the end of the contract sounds early to me. As a matter of fact, you yourself mentioned that you started service on a Friday and they started billing on a Monday, hence the three days (Friday, Saturday, and Sunday) error that you are experiencing. When you think about it, it sounds like they gave you three days for free at the beginning of your service.
There are rules for a reason. You found out that you broke one of their rules. They hit you with a fine that they identified when you signed up. It doesn't matter if you cancel three months into the contract or three days to the end of the contract. When you break the contract you pay the fine. Simple as that. You keep on mentioning that they didn't lose anything for the three days that you canceled early, but you're missing the point.
As I recall, you also mentioned that you didn't keep all of your paperwork. Bad idea. You should always keep everything, just in case. It sounds like it's too late for negotiations. Good luck, but you might as well pay the fine.
Semper Fi 3/2/2
"Wow" is now overused. Therefore, I will use "Magic bananas" instead.