Uh, it sounds to me like the accident didn't happen on the day the shop needed to be done. The accident was previously, the car was in the shop being repaired and was not done in time for the shop.
So she asked for an extension until Saturday (why not Friday?) and since that is the very last day of the month, the scheduler couldn't take a chance that there would be a further delay so they pulled the shop from OP and gave it to someone else.
Devil's advocate here ... it wasn't a great idea to schedule a shop for the day after the car was supposed to be done in the first place. Ever hear of Murphy's Law? Maybe you've never had a car repair before, but delays are common because sometimes you get into the job and -- oops, that thing over there is broken too -- so now they have to order another part.
did you have no options for borrowing a car, renting a car, taking a bus, or any other way to get to the shop? Or did you just figure, what's the big deal, it's another two days?
Does your insurance not provide for a rental car during repairs?
I'm just trying to get you to see what the scheduler was thinking when she decided you were a flake. An accident is an emergency; the repair of the car after the accident is not.
Time to build a bigger bridge.