In warm weather, use heating coil for hot water or hot water heater?

Question:Recently I replaced my oil burner with a new one. The salesman suggested that I add the heating coil to it that would also supply the hot water. This way I wouldn't need to use the gas fired hot water heater that I already had and the water would be heated practically for free since it's being heated within the burner itself. Then when I no longer need heat, I could switch to the hot water heater to supply the hot water and wouldn't need to have my oil burner on at all. This sounded like a great idea.
I spoke to another guy in the heating biz who told me that I should never shut off my oil burner. This made me wonder if I should use the hot water heater at all if I have to keep the oil burner on.
Any suggestions? Does any of this make sense? Still using the oil burner right now but would love to make an informed decision.
Thanks!

Answers:
Shut off your oil burner. You are wasting energy in my opinion.