Only that's bollocks. That rule actually pertains to bleves. These are 'boiling liquid expanding vapour explosions' and are highly destructive, it says here. Firemen have a 'rule of thumb' for these where if the scene is too big to cover with a thumb held outstretched, then you're too close. Even a small bleve (from say a propane cylinder) can fling debris half a mile.

In the instance of mushroom clouds the official line is to seek shelter for a number of very pertinent reasons. First of all unless the curvature of the earth was between you and the cloud, it would most likely always be bigger than your thumb. Secondly, the blast wave would have knocked over trees and telegraph poles even up to thirty miles away, impeding your exit. Thirdly, you don't want to be outside when the next one goes off owing to thermal pulse that can scorch you or blind you up to dozens of miles away. Fourth, the wind direction might actually be taking the fallout away from you and you may evacuate into the shadow of another mushroom cloud fallout zone. Fifth, fallout zones can spread hundreds of miles, especially from ground bursts. Sixth, seeking shelter for a period of several weeks away from the dust if possible is infinitely preferable to stumbling around in it.

That man is needlessly endangering people's health during nuclear armageddon!