Is earthing required for a submersible water pump?
If earthing is provided, earthing should be used.

And a device-local earth is not sufficient.  Imagine if a fault develops inside the device, and the only way for the current to get out and to ground were through the water outlet.  As soon as you use the tap - zap.

Also, as with all devices in such an environment, an ELCB (Earth Leakage Circuit Breaker) should be used.  This monitors current in the earth wire, and if any current is found on that wire it cuts off the power instantly.

Did you know: Water is a very poor conductor of electricity.  Pure water will not conduct at all.  It is actually the impurities and minerals in the water that provide the conduction.