Definitely report to your insurance OP.
I once had a girl hit my car just as I was walking away from it. I heard the bang, and turned around to see her trying to drive away, but she couldn't get out of the space quick enough. I hammered on the window of her car, and told her she'd just hit my vehicle. She got out, together with 2 friends, and told me she was going to take a photo of my car, as she didn't think she'd caused any damage. She told me that she was a nanny and was driving her employer's car, so I said "fine, if you're taking pictures of my car I'll just take a picture of you if that's OK, just in case your employer refutes any claim as it wasn't them driving? She didn't argue, so I took a pic. Just as well I did, as when the insurers found that there was damage to my car, and went after her insurers for payment, her employer denied all knowledge. I wrote to my insurers, enclosing a photograph of the nanny, explaining what she had said at the time, and lo and behold, her employers, suddenly agreed their insurer should pay!
The point I'm trying to make, is that people will almost always try to wriggle out of paying for the damage they've caused to someone else's property, so please don't take what your DH thinks is the 'easy way out', as it won't be. The fact that she drove away without telling you she'd hit your car, and hasn't informed your neighbours that she hit their visitors car, also goes a long way toward going to show she'll wriggle out of paying if she possibly can, so just don't trust her!