"Fender-bender" type accidents happen all the time. Usually there's little obvious damage done: Maybe a fender is crushed and a headlight gets broken. Everybody on the scene usually seems fine and no ambulances are called. One of the drivers will probably end up with a ticket, based on the best judgment of the officer who responds to the scene about who caused the accident to happen.
After a car accident, why do some insurance companies seem like they make a fair offer to some people and not others? Two people could have nearly identical injuries, and the same insurance company will offer one person a reasonable settlement that includes an appropriate amount for their pain and suffering while offering the other person just enough to repair their car.