Can you still go through insurance if the guilty party has tried to pay the autobody repair shop by credit card?

Yes, as long as there is a police report and all repairs have been documented, pictures invoices of parts used ect. This answer "yes" does have its limitations based on the laws of the state that the accident occured. I own a shop in New Jersey and have helped many customers resolve accident related difficulties with little to no problems. A GOOD Repair shop will help you resolve this matter. Good Luck!