It is only during the time that the power is 'off' that the computers can reset their calculations for the next 'run' sequence.
AND on page 5-8 of your owners manuel it states "Turn off your engine when you are refueling"

 

It's not being powered down it's being powered up. On system startup it uses the last map and all parameters zeroed from there.

 

For one thing; your car is ripe fruit to car jackers at a fuel stop. For another the fire hazard. That is some of the danger and the reason for it being illegal.
The computer knows when there is a refueling event if the engine ius off; some of the OBD2 tests depend on a fueling event, the computer determines the alcohol content based on fuel level (it does the calculation after a refueling event).. The EVAP tests rely on knowing when and how much fuel has been added. When the engine is running the EVAP system is trying to not vent the tank and the purge is sucking air not fumes. There are other reasons. This is the 21st century, the computers are taking over.

A fueling event is when the engine is off and the fuel cap is off and fuel is added.

 

Found this TSB. A little heavy for do-it-yerseffers but might facilitate better understanding of why this code can be so difficult if nothing else. I wish I would have had it to print out for my garage before they ran the (fruitless) smoke test.

https://static.nhtsa.gov/odi/tsbs/20...11927-9999.pdf