professor What is insurance, seriously?
In this context it's a transfer of risk of financial liability from the driver(s) to the company for a specified premium. In general, it's a risk transfer method, usually an agreement to compensate a party for a financial loss under defined circumstances.
Lots of companies suck and work to avoid paying claims. Plenty are fair. My company is annoyingly generous with claim settlements, to our detriment in many cases.
Lots of people suck too, like the guy in front of Toulon's wife in the example above. It makes sense that companies would get cynical and defensive over time when there are so many people that treat a minor car accident as a financial windfall.