Sometimes these cash settlements are used to avoid insurance premiums being raised because of submitting a claim. But that defeats the reasons why we have insurance int he first place. In lots of cases, a minor dent (in the more recent cars) can cause thousands of dollars of repair just in labor alone - most people I know, including myself, cannot fork out that kind of cash at once - I would submit the claim to insurance, and even if my rates went up, it certainly would not equal what was being paid out for a claim.
Many times, even the gentlest "bump" can cause a tremendous amount of damage to other components in cars these days ... problems that may not creep up for up to a year, but will have been directly caused by that innocent "bump" that you got $5 for from the other party. Force the claim to be filed ... if there is other related damage farther down the road in time, you'll still be covered and won't have to worry about contacting (again) the person who hit you in the first place ... they may deny that they have even met you or had an accident - then you are out the money from your own pocket and have to get the repairs done yourself. Always, file an insurance claim, no matter how little damage is showing - and always call the police and have a report filed.