Tata Motors Commercial - Service centre damaged my car

I had given my car to an authorised TATA service centre (Malik cars Bowenpally) on **th June for general service. Later on **th June i received a call stating that my car (TATA Nexon -****) had met with an accident due to tyre burst while an ongoing test run. Yesterday when i visited the service centre i was shocked to see the damage done to my car and it was obvious that the car was at high speed and not **kmph mentioned by them.
The service centre GM and the employee are now insisting me to claim my insurance for damages and have denied repairing at their own expense.
Why i should bear the pain and claim my insurance when its clearly a miss from their end? And I'm pretty sure that even after repair this car will have many issues in future, all of which would be borne my me. This is an unnecessary hassle and waste of my time and money for something they should take ***% responsibility for.
I demand to fix my car at their own expense and take responsibility for any issues with the replaced parts in future else provide me a new car. I need my car in the same condition as i have handed over to them.