Leaving it in the on state means its a constant level of energy consumption and probably more efficient than stop starting, like aggressive accelerating and braking in a car drinks more fuel than driving at a steady speed.

Why you'd need a timer? Depends on the age, how sophisticated your system is I guess but people will always want to have that control whether it be setting the heating to come on at set times or just keeping the hot water and central heating settings seperate.

Honestly mate I aint got a fucking clue but my answer sounds pretty plausable. That said the guy could be a complete chancer and has fed you a load of flannel.

How was his arse crack?