I am not an attorney or know anything...but if the dealer did not have you sign the paperwork or provide proof of insurance properly...was the car even yours during the theft? I am sure that is why they hurried over to YOUR HOUSE to have you sign it all real quick. My guess is that likely have accountability in your insurance issue and are trying to clean up their side. Hopefully you put the actual date when you signed and didn't let them back date.
I would be careful to have all communication with both insurance and dealer in writing from this point forward. I would also write out a timeline of all the events so you have something to refer to as time goes on.