Subsection 240.4(A) addresses the power loss hazard and is an alternative to the general rule of Section 240.4. For example, loss of power to a fire pump might be a greater hazard than overloaded conductors supplying a fire pump. 

For a fire pump, the Code requires that the circuit overcurrent device must be sized to allow the fire pump to run to failure. The circuit must stay online while a fire pump is drawing locked rotor current, so the only protection that's actually required (or permitted) is short-circuit protection.

Of course, since this short-circuit device responds to high currents, it will likely provide some protection from other high currents such as ground fault current.