Being Sued??

Back in July 2017 my husband and a lady backed into each other leaving walmart, they took each other's info and went their seperate ways, husband called our insurance and they deemed it both their faults and said that each person should take care of their own vehicles, he told the woman what he heard and she said ok and we never heard from her again, about 2 months later he gets a random call from HER insurance with some snippy lady on the line demanding all of his insurance information so he gave it to her, told her what his agent said and then called his agent when he got off the phone with her, husband gave his agent the # that called him and he said he would deal with them and that was the last we heard until TODAY (9 months later, 11 months after the accident) we get a letter from a lawyers office with this fucking insurance company as their "client" demanding AGAIN our insurance info and $564, my only guess is this bitch made a claim with her insurance even though she was equally at fault and now this insurance company wants us to pay them back the money they gave her when we spent our own money to fixed the damage she caused to ours

Can they do this?? Do we have a solid argument to fight this??