2001 Isuzu Trooper Please Help! 2001 Isuzu Trooper Transmi

Quick story: My wife was driving our Isuzu Trooper and rear-ended someone. $3500 damage to our car - radiator was damaged but transmission seemed fine. Took it to the repair place and they fixed the bumper, radiator, etc. I drove it away and could immediately hear a "whine" in the engine but thought it was just from new parts or something. Within 24 hours, the car wasn't drivable. Took it back to the repair shop and they told me my transmission was shot but that it didn't have anything to do with the accident and showed me pictures of all of the burnt up fluid that came out of it. Repair place is telling me that I'm going to have to pay up to get it fixed because it wasn't their fault. My insurance is saying they won't pay for it because it wasn't part of the accident.

Keep in mind though that I have never had any transmission problems with that car including and up until the day of the car accident. Not only that, but I have a receipt showing that I had the transmission fluid checked (and the lube shop confirmed that they check quality and color of the fluid) just two weeks before the accident.

How possible is it that the repair place accidentally allowed too much transmission fluid to leak out when they were repairing the radiator and consequently burnt up the engine (they tell me only an 1/8 of a cup of fluid would have leaked out) but are now showing these pictures that came from who-knows-where so they can back up that there was plenty of transmission fluid in it and it wasn't their fault?

Also, is it possible that when the accident happened, the transmission was jarred and corrosion came loose and mixed in with the fluid to cause it to be in such bad shape?

Any ideas on what happened here? Part of the problem too is that I don't exactly remember when I last had my transmission flushed and I don't have a receipt on it. Any help you can give is much appreciated. Thanks.