Earlier quoted context omitted.
Sounds like both players didn't die at the same time then.
I think there is an edge case where both people die at the same time, but one is about to make a move and drops the piece as they die, and it lands on the board. Is that move valid? Or not as they are already dead when it lands?
However, I can see a situation where the player dies and falls on the clock, pushing his button.