There is absolutely no evidence this is true. There are always a few first generation talents who build empires from dirt and nothing (for values of nothing that usually include war, grift, and slavery).
But once an empire is established it becomes largely self-sustaining, and the inheritors get a huge head start over everyone else in their cohort.
Inherited wealth is not self-sustaining at all: if you spend it down, it disappears. Most inheritors of large windfalls will not manage to pass down that wealth in turn; it takes a rare ingrained cultural attitude to make it genuinely "self-sustaining", and even then that really means leaving the wealth as it is and managing it well - not using it to pursue any immediate "head start" in living standards over your peers.