Years ago my daughter backed her car into my popup causing SIGNIFICANT damage. The insurance company (GEICO) did NOT total it. After repairs, which looked good, we had all sorts of unanticipated problems for years and years down the road. Trailers are surprising in terms of how they respond to various stresses and strains going down the road.
My advice - if they are willing to total it, accept it and move on. Get a new trailer. You'll never know what hidden problems you will have avoided, but know that they could be significant.
-Speak