Conversely, with the engine shut down there is no way that fuel can make it past the engine-driven fuel pump to the fuel control and then to the nozzle screwed into the burner can.
FH1100
Well I can tell you that I have filled the burner can full of fuel on a jetranger when attempting to drain the A/F fuel filter ( boost pumps on, Battery on, Throttle left in full open position). The Owner & DOM of the company I worked for interrupted me in the process and after talking for a moment we all heard fuel spilling all over the hangar floor which was draining out of the burner can. So we had to wheel it outside pulled the IGN breaker and motored the starter a couple times waited a bit then perfect start.
I am not saying you are wrong and I am no AME just a pilot, but I do know the difference between the A/F fuel filter and burner can. And no, definately not confused.
Another thing for new pilots to watch out for is when draining the fuel from the A/F fuel filter be careful that the boost pumps are on and that the drain valve is closed after draining If the boost pumps are off and drain valve locks open and not noticed when you start the aircraft you will have fuel draining out of the helicopter and I have heard of pilots taking off with the drain valve still open.