Is insurance weird in Florida? In most states I know of your insurance takes care of you and then hashes out the details with the other vehicle's insurer. At least that's what happened in the few situations I or family members have had.
I'd recommend reviewing up your local laws and negotiating accident settlements with insurance companies yourself unless there are physical injuries involved or need to take someone to court.
I imagine similar situations occur in Austria or Germany, wherever people and profit are involved really.
what you are saying sounds like that if you don't pay attention in advance or you trust your insurance company you loose out.
that should not happen.