I can justify that statement.
The immersion heater replaces heat lost by using the hot water for baths/showers/washing up/etc. It also replaces the heat lost from the water stored in the tank. No matter how well insulated the tank is, it will lose heat. The rate of heat loss is proportional to temperature (Newton's Law of Cooling), therefore the rate of heat loss reduces as the temperature in the tank falls. Leaving the immersion on continuously keeps the temperature high and therefore keeps the rate of heat loss relatively high.
Unless your tenant is smarter than Newton, he is talking out of his bottom.