I see they gave the misleading explanation that larger phase conductors somehow cause greater fault currents. There is a kernel of truth to this, in that greater conductor resistance/impedance reduces fault current, and therefore greater conductor size might seem to mean greater fault currents. However, the same result can happen with a shorter length circuit to begin with.
In any case, larger conductors do not increase available fault currents to any greater value than the available fault current already was, at the origin of the circuit.