Rear ended a foreign driver

This happened in CA, on the freeway today.

Someone slammed the brakes hard, which caused the driver in front of me to brake suddenly as well. I wasn't able to stop in time and ended up rear-ending the driver.

No injuries at all, the front side of my car suffered some damage (broken Benz logo/ cracked front trim), but nothing crazy.

The rear bumper of her (driver in front of me) car suffered a decent number of scratches and chips on the paint, and it also looked like the lower rear bumper had shifted out of place a bit.

She wanted to settle this privately, providing me with her phone number and ID (however, it was a Venezuelan ID, not even a driver's license), and sort of changed topics when I asked her to exchange insurance policies with me. I gave her my number in return, and she took a photo of my license.

How should I go about handling this? I'd preferably not want to contact my insurance because I'm relatively certain I'd be held at-fault since I rear-ended her, regardless of the circumstances. Would it be safe to handle it privately, and what steps should I take to make this go over smoothly