Stay skeptical around overly generous motorists. One example might be a merging situation in which the driver signals his intent to willingly yield to give you the right of way. Then he speeds up, a sideswipe occurs, and when the police arrive, he denies ever giving you any such signal.
Possibly easiest of all are "paper accidents", where the cost of accidents are simply exaggerated on paper (by a shady body shop) or fabricated altogether. Perpetrators typically keep claims under $1,000 so insurers would be less apt to investigate. Which is what makes it so easy.
If cautious, preventative driving doesn't work, then in any incident, the smart move is to document the responses, driver's licenses, and plate numbers of everyone and everything, take a photo or two if you have a camera handy, and call the cops right away. If the other guy wants to lie, make him lie right there, unrehearsed, for the official record, to the face of the law. If anything comes up, it will be easier to fight it then.