Obviously the black box can only record what the computer tells it is the state of the switches. There's no camera looking at the switches to confirm they actually were moved. No doubt the switches are wired such that a short or an open circuit will not fool the computer into thinking the switch was moved and shut the engines down. But if something caused the computer to think (pardon the expression) the switches had changed state, it would shut the engines down and the flight recorder would dutifully record this change of state.
Suppose for a moment a computer glitch did shut the engines down. The pilot, upon noticing this asks the copilot about it and he says, no I didn't shut them down. Knowing he has to do something, reaches over, flips them to off and back to on again to try to get them going again, after which the engines did restart but sadly not in time to prevent disaster.