The deal with shutting engine off goes back to early days when fuel tank was under the front cowel directly behind the engine. There's no danger in fueling with engine running. Unless you're smoking while fueling, that's another story all together.
2012 F250 Lariat 2WD long bed 6.7 Power Sroke. Great truck. Used primary for towing 5th wheel Rv. Sold both. Purchased '22 Maverick Lariat EB and love it.
Have over 30k using dolly behind 32' class C. 2.0 EB. No issues after initial lesson oon turning off auto brake lock. Keeps mileage off front drive. Can't flat tow EB. I'm 76 y.o., the trailer dolly is a good idea, thanks.
Better fuel mileage in tow/haul mode. Transmission shift points change. I also use the manual shift mode to save on brakes. Just traded for the new Godzila V8, what a difference! 2mpg better and much more torque. '22 Lariat/'24 Jayco Greyhawk 29MV.
Have one in my 22 Lariat EB. Love it. Store my jumper cables, tie down straps, trailer hitch and misc. Stuff. Only issue is have to remove it sometimes when needing entire bed space. Unlocks easily and just raise rear seat for temporary storage of it.