The schematic is simple yet portrays the system well.
Transfer hoses come from the trans pumps and are connected to each other, and in turn to the supply tanks. It seems to me that if there is a leak or failure anywhere in the flexible transfer hose, the fuel will end up being circulated within the main tank and perhaps not be able to top up the supply tanks fast enough to prevent them emptying.
The check valve is integral to the transfer pump unit.
But of course, if this was to have happened the engines wouldn't have stopped at the same time and the fuel warnings and gauge would have indicated something to the crew.(therefore this part of the thread is imho better off being in the 135 thread)