As someone who works in the fuel industry (not aviation) I find it amazing, almost medievil in terms of health and safety, that planes are allowed to be refuelled with people on board. I know of no other area of fuel supply/distribution where this would be permitted!!
Despite what has been said here, including by me, the situation especially with Jet A1 is relatively safe.
I would be more worried about people at the local service station, filling their car with petrol while the kids are strapped inside the car.