IIRC, once you’ve accepted money, the claim is deemed to be settled so if you later discover that the frame is cracked, you won’t have any recourse to further action.
That said, if it’s a genuine “oops” moment, the driver was contrite, there’s no real damage then yes, I’d just take the money.
I had similar once with a driver who pulled out on me on a roundabout, I swerved to avoid and came off. Didn’t actually hit the car. She stopped, she was absolutely mortified and to be fair I looked worse as I had a cut above my eye where my glasses had dug in so there was a line of blood down my face. Witnesses (including a work colleague as I’d only just left the office) and she immediately accepted full responsibility, offered to pay for everything, gave her details in front of all the witnesses. As it turned out it was just a damaged helmet and her actions were all above board. It was a genuine “didn’t look closely enough” moment and she was so apologetic.