Exorbitant payments for third party claims

Some motorists were surprised to learn about the large sums paid by their insurers for third party claims. In some cases, the third parties were also at fault, but the insurer paid anyway. In many cases, the amounts paid were exorbitant, e.g. $5000 or $10,000 for a minor damage. The high payments lead to high premium rates and loading on renewal.
Have you experienced this yourself or know of friends who suffered this fate? Share your views here.