"like quality" sure sounds alot nicer than outright "used" parts.
to me it sounds like the repair center wants the insurance company to dish out MORE by saying you need new parts and warranty. giving you the run around.
if your car was new or close to new, i would push the insurance company to dish out the extra funds needed. but since its not so new, "used" parts would seem to fit the description for the "like quality" of your car
IMO if the repair center really doesnt want to do the work covered by insurance, take it elsewhere. it sucks that its draggin for you though, good luck!