Your analogy falls apart in that an electric water heater is more like a thermos than a teapot.
It takes a certain amount of energy to raise the water a degree ... 2.42 watts per gallon. If you have to raise it 10 degrees, it doesn't matter if the heater comes on ten times to raise it one degree, or if it comes on once to raise it ten degrees. You use the same energy to recover the 10 degrees of heat you lost.
If you are getting standby losses through the jacket and save money by turning it off for 8 hours, you should definitely take the other, cheaper measures anyway. No matter when you heat the water, the heat loss is still happening. There's a good chart with formulas and facts at this
PDF file link
Here's a quote from another website:
From
http://michaelbluejay.com/electricity/waterheaters.html
You pay for electricity by the kWh, so if you are paying .08 per kWh, your monthly savings with a newer heater is only 1.12 per month. A $40 timer has a payback of about 3 years, and much longer if you pay an electrician to put one in ($80 to $120 in my area).
There is a point where turning it off will save money even with a well insulated tank, but that shouldn't be within 8 hours. If your friends are saving money over that short a period of time they still have a great opportunity to save money (and energy) by insulating the tank and pipes.