In addition to what nanoman said, there's the factor that someone coming after you very well might choose to accept the policy limit with less of a fight rather than going after you in what's basically guaranteed to be a hard fight.
The insurance company will be looking at what they would spend in legal bills vs the chance of reducing the judgment. However, if they're after well above the policy limit the economics for the person become different--the total loss is capped at their assets, whether it's spent on a judgment or legal bills. Hence the individual will likely fight very hard even on cases they have little chance of winning.