Car Accident

I 20(f) was rear ended while I was at a stop sign. Safeway insurance (the persons insurance that hit me) said they "are not obligated to cover" if I take it to the Hyundai collision repair center. That's bs. They won't let me pick my body shop. I talked to a Hyundai representative today and she stated if I took my Hyundai Elantra 2023 that has a 10 year warranty to a non Hyundai shop to get repaired than my warranty will be canceled. Can someone please help me. Im fighting tooth and nail with these people. Is this true??