In the absence of a thermometer, a rolling boil is the only way to judge water temp accurately. That's the real reason for appealing to it.

Water boils at 212F at sea level and 203 at a mile. Water above 70C (158 F) will kill most water-bourne pathogens. However, it takes a few minutes, so taking the time to bring water to a boil and letting it cool to a drinkable temperature finishes the job. There are a few nasties that will survive such as botulism, but it is a problem only if you are canning something - not in your regular cooking.