Car accident advice

Anyone that could provide me some advice would be greatly appreciated.

I am in florida and was turning right and a pedestrian stared to cross the street in the intersection. So I stopped to let them pass and was rear ended. I had my turn signal on but the other driver claimed I didnt. There was a grainy video of the intersection but it isnt clear enough to show the car lights. For example you cant see headlights, brake lights, or anything from not just my car but any. In the police report he wrote "didnt see a turn signal" which is accurate but not because it wasnt on but rather the video is poor quality. He couldnt tell if it was on or off. Anyways I filed a claim on their insurance (they have been nonresponsive) but they did the same on mine and mine wants me to take 20% responsibility. They dont understand the nuance in the police offiecers statement.

My company is now saying that if they take the 20% responsibility then my claim has to go through my company….and I am hit with my deductible and since I dont have rental coverage I'll be out of pocket for that as well. So I am guessing I will be out $2k as it will take time for the car to get fixed for an accident that I had no responsibility for.

The other car was 10 years old so I assume they only have the basic insurance. Also this guy has a crazy arrest (and driving) record. Im confused as to why my insurance wants to take any responsibility.

So my question here – should I just use my own insurance and deal with being out the $2k or do something else?