Nice try, I ain't buyin' it.
On the serious side, if you were in a situation where your car won't restart, and your going cross country, this is sort of an emergency situation in which you can't in practicality repair it, carefully refill with engine running.
If you're just leaving the engine running to keep the inside warm on a winter day, come on, why take such a risk. Also someone pointed out the possibility of getting it stolen while paying. About 20 years ago, my Dad got his brand spanking new pick up with lots of tools and expensive stuff inside, stolen almost the same way. He was standing inside the service station office ten feet from the truck telling them he was leaving a tire to be fixed. As he walked out the door, someone drove it away with him yelling obscenities at them. He hasn't seen it since.
Is keeping the inside comfortable worth taking such a chance? With a diesel, I think the chance is almost non-existent. Given the volatility of gasoline, on the other hand, I'm not doing it. I'm a country boy, and as a kid started trash fires with gasoline. Maybe under CERTAIN conditions you could put out a cigarette in gasoline, but I'm not trying that or anything else while standing over 18 or 20 gallons of the stuff.
If you've never started a fire with gasoline, I wouldn't recommend trying it, just to find out how quick the stuff goes up. Take someone's word for it.
But if your suicidal tendencies are stronger than your survival tendencies, I say Go For It.
Best of luck to everyone on this,
'01 C Class, Six Speed
'84 Euro 240D, manual, 533K miles
'88 300E 5 Speed
'81 300D Daughter's Car
Over 800,000 miles in